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We have,
sin2 72° - sin260°.
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
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°
L.H.S = cos78°.cos42°.cos36°
L.H.S = cos 6°.cos 42°.cos 66°.cos 78°
L.H.S = sin 6°.sin 42°.sin 66°.sin 78°
L.H.S = cos 36°.cos 42°.cos 60°.cos 78°
sin36°.sin72°.sin108°.sin144°
[∵ sin144°= sin (180° - 36°) = sin36° and sin108° = sin (180° - 78°) = sin72°]
= sin 36°.sin 72°.sin 72°. sin 36°
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Chapter 9: Trigonometric Ratios of Multiple and...