How do you verify $(sin θ - 1) (tan θ + sec θ) = - cos θ$ $(sintheta-1)(tantheta+sectheta)=-costheta$ ?

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Answer 1 · 2016-11-14T19:43:12

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$(sin θ - 1) (tan θ + sec θ) = - cos θ$ $(sintheta-1)(tantheta+sectheta)=-costheta$

Left Side : $= (sin θ - 1) (tan θ + sec θ)$ $=(sintheta-1)(tantheta+sectheta)$

$= (sin θ - 1) (\frac{sin θ}{cos θ} + \frac{1}{cos θ})$ $=(sintheta-1)(sintheta/costheta+1/costheta)$

$= (sin θ - 1) (\frac{sin θ + 1}{cos θ})$ $=(sintheta-1)((sintheta+1)/costheta)$

$= \frac{{sin}^{2} θ - 1}{cos θ}$ $=(sin^2theta-1)/costheta$

$= \frac{- (1 - {sin}^{2} θ)}{cos θ}$ $=(-(1-sin^2theta))/costheta$

$= \frac{- {cos}^{2} θ}{cos θ}$ $=(-cos^2theta)/costheta$

$=(-cos^cancel2theta)/cancelcostheta$

$=-cos theta$

$:.=$ Right Side

How do you verify (sintheta-1)(tantheta+sectheta)=-costheta(sinθ−1)(tanθ+secθ)=−cosθ(sintheta-1)(tantheta+sectheta)=-costheta?