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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.1

 

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

L.H.S = sin2 24° - sin2

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

= sin 30°sin 18°

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

= 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°

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

= RHS

 

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

L.H.S = cos78°.cos42°.cos36°

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

= RHS

 

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

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.6

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

 

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

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

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

= 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°

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

= 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°

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

= 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°

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

= RHS


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