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prove: sinθ cosθ = (cosθ - cos^3θ)/sinθ

0 votes
i need all steps.
asked Mar 10, 2014 in TRIGONOMETRY by dkinz Apprentice

1 Answer

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Remember the formulae

Sin^2Ѳ+Cos^2Ѳ = 1

CotѲ = CosѲ/SinѲ

Right handside identity

= (CosѲ-Cos^3Ѳ)/SinѲ

= CosѲ/SinѲ - Cos^3Ѳ/SinѲ

= CosѲ/SinѲ - Cos^2ѲCosѲ/SinѲ

= CotѲ - Cos^2ѲCotѲ

= CotѲ(1-Cos^2Ѳ)

= CotѲSin^2Ѳ

= (CosѲ/SinѲ)Sin^2Ѳ

= CosѲSinѲ

= Left hand side identity.

answered Mar 10, 2014 by david Expert

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