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Prove

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sin^5(x)=(1-2cos^2 x +cos^4 x)(sinx)?

asked Nov 20, 2014 in TRIGONOMETRY by anonymous

1 Answer

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Left hand side identity = sin5(x)

= sin(x) sin4(x)

= sin(x) [sin2(x)]2

{Apply Pythagorean identities sin2x + cos2x = 1}

= sin(x) [1 - cos2(x)]2

= sin(x){1 + [cos2(x)]2 - 2cos2(x)}

= sin(x)[1 + cos4(x) - 2cos2(x)]

= [1 - 2cos2(x) + cos4(x) ][sin(x)]

= Right hand side identity.

answered Nov 20, 2014 by david Expert

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