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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, = 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