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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,

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

= 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,

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

= tan θ = RHS

 

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

LHS,

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

Dividing numerator and denomenator by cos θ

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

 

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

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.8(i)

 

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

LHS,

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

= 2

= RHS

 

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

LHS,

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

= 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)

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

= RHS

 

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

LHS,

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

= RHS


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