Question

Verify seca(1-sina)(seca+tana)=1

Answer 1

That is an interesting question
Here is how to reach it....

Refer to the pic I attached
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I hope that helps!

Answer 2

seca(1-sina)(seca+tana)=1
Left hand side
=(1-sina) (seca +tana) / cosa
=seca +tana - sinaseca - sinatan / cosa
=seca + tana -tana -(sin^2a/cosa) / cosa
=(1/cosa - sin^2a/cosa) / cosa
= (1-sin^2a / cosa) / cosa
= (1-sin^2a)/ (cos^2a)
=1 (verified)