# Introduction to Trigonometry – Class X – Part 8 | Exercise 8.4 Q4- 5 (iii) Solved

### Watch the eight video session on “Introduction To Trigonometry” for Class Xth – concepts and solved questions

Introduction To Trigonometry – Class X – Part 8

1. Trigonometric identities that are in syllabus (class 10, NCERT):

sin²θ + cos²θ = 1

1 + cot²θ = cosec²θ

1 + tan²θ = sec²θ

2. How to remember trigonometric identities: As explained in the video, just remember the first one i.e sin²θ + cos²θ = 1

a) The second one (1 + cot²θ = cosec²θ) can be derived from the first by dividing both sides by sin²θ.

b) The second one (1 + tan²θ = sec²θ) can be derived from the first by dividing both sides by cos²θ.

3. Usually the concepts of “trigonometric angles for complementary angles” and “trigonometric identities” are tested together in exam questions.

NCERT Exercise 8.4 Q4- 5 (iii) Solved

4. (i) 9 sec²A – 9 tan²A =

(A) 1 (B) 9 (C) 8 (D) 0

(ii) (1 + tanθ + secθ) (1 + cotθ – cosecθ) =

(A) 0 (B) 1 (C) 2 (D) –1

(iii) (sec A + tan A) (1 – sin A) =

(A) sec A (B) sin A (C) cosec A (D) cos A

(iv) (1 + tan²A)/(1 + cot²A)

(A) sec²A (B) –1 (C) cot²A (D) tan²A

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

(i) (cosec θ – cot θ)² = (1 – cosθ)/(1 + cosθ)

(ii) cosA /(1 + sinA) + (1 + sinA)/cosA = 2 secA

(iii) tanθ/(1 – cot θ) + cotθ/(1 – tanθ) = 1 + secθcosecθ

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