Chapter 9: Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.1

We have,

= tan θ = RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.2

LHS,

= cot θ = RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.3

LHS,

= tan θ = RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.4

LHS,

= 2 cos θ =  RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.5

LHS,

= tan θ = RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.6

LHS,

= tan θ = RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.7

LHS,

Dividing numerator and denomenator by cos θ

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.8

Dividing numerator and denominator by cos θ/2

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.9

LHS,

= 2

= RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.10

LHS,

= 1 + 1

= 2

= RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.11

LHS,

(cos λ + cos β)² + (sin λ + sin β)²

= cos² λ + cos² β + 2 cos λ cos β + sin² λ + sin² β + 2 sin λ sin β

= (cos² λ + sin² λ) + (cos² β + sin² β) + 2(cos λ cos β + sin λ sin β)

= 1 + 1 + 2cos (λ - β)

= 2 + 2 cos (λ - β)

= 2(1 + cos (λ - β)

= RHS

 

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.1 – Q.12

LHS,

= RHS