How do you verify $(sintheta-1)(tantheta+sectheta)=-costheta$ ?

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Answer 1 · 2016-11-14T19:43:12

see below

$(sintheta-1)(tantheta+sectheta)=-costheta$

Left Side : $=(sintheta-1)(tantheta+sectheta)$

$=(sintheta-1)(sintheta/costheta+1/costheta)$

$=(sintheta-1)((sintheta+1)/costheta)$

$=(sin^2theta-1)/costheta$

$=(-(1-sin^2theta))/costheta$

$=(-cos^2theta)/costheta$

$=(-cos^cancel2theta)/cancelcostheta$

$=-cos theta$

$:.=$ Right Side

How do you verify (sintheta-1)(tantheta+sectheta)=-costheta(sintheta-1)(tantheta+sectheta)=-costheta?