Chapter 9: Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.1

We have,

sin² 72° - sin²60°.

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.2

L.H.S = sin² 24° - sin²6°

= sin(24 + 6) sin(24 - 6) [ ∵  sin(A + B)sin(A - B) = sin²A - sin²B]

= sin 30°sin 18°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.3

L.H.S = sin²42° - cos²78°

= sin²(90 - 48) - cos²(90 - 12)

= cos²48° - sin²12°

= cos(48 + 12).cos(48 - 12) [∵ cos(A + B).cos(A - B) = cos²A - sin²B]

= cos60°.cos36°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.4

L.H.S = cos78°.cos42°.cos36°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.5

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.6

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.7

L.H.S = cos 6°.cos 42°.cos 66°.cos 78°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.8

L.H.S = sin 6°.sin 42°.sin 66°.sin 78°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.9

L.H.S = cos 36°.cos 42°.cos 60°.cos 78°

= RHS

Trigonometric Ratios of Multiple and Sub Multiple Angles – Exercise 9.3 – Q.10

sin36°.sin72°.sin108°.sin144°

[∵ sin144°= sin (180° - 36°) = sin36° and sin108° = sin (180° - 78°) = sin72°] 

= sin 36°.sin 72°.sin 72°. sin 36°

= RHS