# 10th Maths Chapter 6 Trigonometry Exercise 6.1

10th Standard Maths Chapter 6 Trigonometry Exercise 6.1 Guide. TN SSLC Samacheer Kalvi Guide Chapter 6 Exercise 6.1 Book Back Answers & Solutions. 10th All Subject Guide – Click Here. Class 1 to 12 All Subject Book Back Answers – Click Here.

10th Maths Chapter 6 Trigonometry Exercise 6.1

### 1. Prove the following identities.

• (i) cot θ + tan θ = sec θ cosec θ
• (ii) tan4θ + tan2θ = sec4θ – sec2θ

Solution:

Solution:

Solution:

### 4.Prove the following identities

• (i) sec6θ = tan6θ + 3tan2θ sec2θ + 1
• (ii) (sinθ + secθ)2 + (cosθ + cosecθ)2= 1 + (secθ + cosecθ)2

SOLUTION:

(i) L.H.S = sec6θ = (sec2θ)3 = (1 + tan2θ )3 = (tan2θ + 1)3
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= (tan2θ)3 + 3(tan2θ)2 × 1 + 3 × tan2θ × 12 + 1
= tan6θ + 3tan2θ × (sec2θ – 1) + 3tan2θ + 1
= tan6θ + 3tan2θsec2θ – 3tan2θ + 3tan2θ +1
= tan6θ + 3tan2θ sec2θ + 1 = R.H.S

(ii) L.H.S = (sinθ + secθ )2 + (cosθ + cosecθ)2
= sin2θ + 2sinθ secθ + sec2θ + cos2θ + 2cosθ cosecθ+ cosec2θ

Solution:

(ii)

7.

Solution:

8.

Solution:
(i) LHS:

Solution:

10.