(cos theta-sin theta)(1+tan theta)/2cos^2theta-1=sec theta
Prove lhs= rhs
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(cos theta - sin theta) ( 1+ sin theta/cos theta)/(2cos²theta -sin²theta-cos²theta)
= (cos theta - sin theta) ( cos theta + sin theta)/cos theta (cos²theta-sin²theta)
= (cos²theta-sin²theta)/cos theta(cos²theta-sin²theta)
= 1/cos theta
= sec theta
= RHS
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