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trigonometry

Prove that (1+secθ)(1-cosθ)=sinθtanθ

Posted in Math, asked by malebo, 6 years ago. 1576 hits.

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(1+secθ)(1-cosθ)=sinθtanθ

LHS = (1+secθ)(1-cosθ)

      = (1+(1/cosθ))(1-cosθ) [Since secθ=1/cosθ]

      =( cosθ+1)(1-cosθ)/cosθ [On taking LCM]

      = (1-(cosθ)^2)/cosθ [Since (a+b)(a-b)=(a^2)-(b^2)]

      = [(sinθ)^2]/cosθ [Since 1-(cosθ)^2 =(sinθ)^2]

      = sinθ * sinθ/cosθ

      =sinθ *tanθ =RHS

vinu omanan
vinu omanan - 6 years ago
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