Math: Trigonometric Identities and Tips to Remember


Trigonometry! Some of you may have been practicing trigonometry since 8th grade.. But who really likes trigonometry?

Trigonometry is simple logic and once you get the hang of it, it is a very interesting topic in math! And easy, too!

We all know the basics:

sinA = perpendicular/hypotenuse

cosA = base/hypotenuse

tanA = sinA/cosA

           = perpendicular/base

cotA = 1/tanA

           = cosA/sinA

           = base/perpendicular

sinA = 1/cosecA

cosA = 1/secA

tanA = 1/cotA

Trigonometric Table

Here are the important trigonometric identities you’ll need to memorize (YES, MEMORIZE!):

sin2A + cos2A = 1

1 + tan2A = sec2A

                           To remember this identity, s and t are different letters.

1 + cot 2A = cosec2A

                     To remember this identity, c (cosec) and c (cot) are the same letters and cot is the inverse of tan.

While solving Proving sums in Trigonometry,

Remember:

If you get a question like this:

P.T. (1+cosA)/(1 – cosA) = (cosecA + cotA)2

Observe that the RHS has cosecA=1/sinA and cotA=cosA/sinA

Since both cosecA and cotA, when simplified have sinA as the denominator, if we divide EACH TERM on the LHS by sinA, we will solve the sum.

You can also apply the same technique to proving sums which have cosA as the denominator.

Give it a try!

 

Here’s a link to the PDF file for the above notes:

NOTES – Trigonometric Identities and Tips to Remember

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32 thoughts on “Math: Trigonometric Identities and Tips to Remember

  1. Husain says:

    Hi,I am going to appear for my ICSE board exam nexy yr.I am facing difficulties in studying fundamental identities.I dont know how to prove LHS=RHS.CAn you help?And give me some tips for preparing for the exam.Please!

    Like

  2. Samm says:

    Hey this is Samm here.
    i really like the site and appreciate the initiative you guys have taken. its really helpful.
    I was glad to find out that the 1+tan^2A=sec^2A formula’s shortcut was the way i remembered it too.
    I am confused about the sum you have given for example, as i cannot understand if the lhs (1+cosA)/(1-cosA) or 1+cosA/(1-cosA).
    thank you.

    Like

    • icsehelpline101 says:

      Hi Samm!

      Thank you very much for your kind words. I’m glad you find the notes helpful!🙂

      In reply to your question, LHS=(1+cosA)/(1-cosA). We will rectify that immediately to avoid further confusion. Thank you for pointing it out!

      P.S. Great minds think alike, hence the shortcut strategy.🙂

      Like

  3. Bhoomika Kashyap says:

    I am feeling Trigonometry really very confusing.I know the identities but I am not able to apply it in their appropriate places.Can you please help me in this?Thank you

    Like

    • ICSE Helper says:

      Bhoomika,

      The only way to get a hang of trigonometry is to practice, practice, and practice. Based on personal experience, if you keep practicing, you will gradually begin to know where to apply certain tricks and how to go about solving the question. Try solving questions previously asked in the ICSE examinations. Solve them twice or thrice to get a feel of them. On your third try, you are sure to get the correct answer on your own!🙂

      Like

  4. sidhant humne says:

    Hey! I am really facing huge difficulty in solving trigonometry. I really need help can you please help me. I am not able to solve one some in trigonometry please urgent help required.🙂

    Like

  5. Ansh Agrawal says:

    i have my cbse grade 10 examination day after and i want to know is there any procedure or step which i can follow for trignometry. what i mean by steps is like u know first only multiply then go to this step, if it is not there try this one. so that it becomes easier to solve. the main probem with me is i dont know how to start a question especially the 3 and 4 markers. like u kno which step to do first – convert it to this or multiply by something or what.
    please help me.
    thanks in advance

    Like

    • ICSE Helper says:

      Akshit,
      Another reader also mentioned coming across such a problem where the PDF wouldn’t open. I would suggest that you try opening the file on your computer or desktop. Please let us know if you face further problems.
      Hope this helped! Thanks for visiting!🙂

      Like

  6. Harsh vardhan agrawal says:

    Hey can u plan a schedule for me because my study is not going regular! I m cbse class 10th student and I have to bring 10 cgpa in this session as 10 cgpa is not a big deal in class 10th. I m too much worried about my study because my summer vacations spent and i didnt study much and not regular. So please help me to plan my schedule for all five subjects: hindi english maths science and sst with main attention on 3 subject i.e maths science & sst.I hav 2 tutions for maths and science for 1 or 1 and half hour each. I m worried about sst very much. I have loads of school written work so i cant give time for self study. So help me to prepare well in 2 months. And shud i have to read ncert in science and sst. Well i cant read ncert in sst because its boring and syllabus is lengthy. Thank you

    Like

    • ICSE Helper says:

      Harsh,

      Hi there! Thanks for stopping by.

      Don’t worry about having wasted time.
      “The time you enjoyed wasting is not wasted time!”😉
      On a serious note, we will respond in detail with a draft time table for you, via email within a few days.

      Hope this helps! If you have further questions, please don’t hesitate to ask. Stay connected!🙂

      Like

    • ICSE Helper says:

      Nimisha,

      Hi there! Thank you for stopping by and for the kind words. We really appreciate it.🙂

      Regarding when to use which formula, we suggest you practice as much as you can. Solve and go through the solved examples in your textbook first to get a gist of the topic. Later, practice solving exercises and take note of where you are making mistakes. Keep practicing, ask your teacher for help, and make sure you explore different possibilities and ways of solving the same sum. Again, go to your teacher for guidance.

      Hope this helps! If you have further questions, please don’t hesitate to ask.🙂

      Stay connected!

      Like

    • ICSE Helper says:

      Ashish,

      Hi there and thanks for visiting our blog!

      I would recommend that you practice immensely. As we suggested to another reader, solve and go through the solved examples in your textbook first to get a gist of the topic. Later, practice solving exercises and take note of where you are making mistakes. Keep practicing, ask your teacher for help, and make sure you explore different possibilities and ways of solving the same sum. Again, go to your teacher for guidance.

      A small trick that may help is to simplify the LHS as far as you can and then simplify the RHS so that ultimately, both simplified versions are equal.

      Hope this helps! If you have further questions, please don’t hesitate to ask.🙂

      Like

  7. pranjal says:

    hey there! I m a class 10 student having a desire to get 10 cgpa. i dont know to make a time table can u send it to me pls.
    i dont go to any tutions so i need attention on my studies last year i got 9.4 cgpa help me to get higher this time
    thank you

    Like

  8. Piyush Raj says:

    I found trignometry of NCERT so easy.So i want that i should get more tricky and time consuming questions on this site.

    waiting for a early response.
    THANK YOU

    Like

    • ICSE Helper says:

      Hi there! Thanks for stopping by.

      As mentioned in our tagline and on our About page, we post notes rather than sample questions. Our belief is that one can get hold of questions more easily than one can avail precise notes. Hence, we primarily focus on providing notes and tips to Class 10 students of ICSE.

      We hope you find other relevant material for mathematics on our blog. Glad to have you here! Keep visiting.🙂

      Like

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