In worksheet on evaluation using trigonometric identities we will solve various types of practice questions on finding the value of the trigonometric ratios or trigonometric expression using identities. Here you will get 6 different types of evaluation trigonometric identities questions with some selected questions hints.
1. If 1 + cos^{2} A = 3 cos A sin A, find the value of cot A.
2. If csc A – cot A = \(\frac{2}{3}\) then find the value of the following
(i) csc A + cot A
(ii) csc A
(iii) cot A
(iv) cos A
3. If sec θ + tan θ = x, find the value sec θ and tan θ.
4. If x cos A = 1 and y = tan A then find the value of x^{2} – y^{2}.
5. If sec θ + tan θ = 3, find the value sin θ.
6. If sin A – cos A = \(\frac{\sqrt{3} - 1}{2}\) then find the value of the following
(i) sin A cos A
(ii) sin A + cos A
Hint: Use (sin A + cos A)^{2} + (sin A – cos A)^{2} = 2.
Answers on Worksheet
on evaluation using trigonometric identities are given below to check the exact answers of the questions.
Answers
1. \(\frac{1}{2}\) or, 1.
2. (i) \(\frac{3}{2}\)
(ii) \(\frac{13}{12}\)
(iii) \(\frac{5}{12}\)
(iv) \(\frac{5}{13}\)
3. \(\frac{x^{2} + 1}{2x}\) and \(\frac{x^{2} - 1}{2x}\) respectively.
4. 1
5. \(\frac{4}{4}\)
6. (i) \(\frac{√3}{4}\)
(ii) \(\frac{\sqrt{3} + 1}{4}\)
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