Question

if sin a = 1/2 prove that (3cos a-4coscube a)

Answer 1

sinA(1+sin^2A) = cos^2A

sinA(2 -cos^2A) = cos^2A

Squaring both sides,

sin^2A(4-4cos^2A +cos^4A) = cos^4A

(1-cos^2A)(4-4cos^2A +cos^4A) = cos^4A

4-4cos^2A +cos^4A-4cos^2A+4cos^4A-cos^6A = cos^4A

4 -cos^6A +4cos^4A -8cos^2A = 0

cos^6A - 4 cos^4A + 8cos^2A = 4

Hence Proved.

Answer 2

Hey
Here your answer
☺️☺️☺️☺️☺️☺️☺️☺️☺️☺️
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3cosa - 4 cos^3a
= cosa (3 -4 cos^2a)
= cosa {3 - 4(1 - sin^2a)}
= cosa (3-4 + 4 sin^2a)
= cosa(-1+4×1/4)
= cosa (-1+1)
= 0

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Hope it helps you