Question

Prove the following


$\sf {sec \theta + tan \theta = cos / 1 - sin {\theta}}$

Answer 1

here your answer sir ihope you like my answer sir


Explanation:

(secθ+tanθ)(1−sinθ),

=(1cosθ+sinθcosθ)(1−sinθ),

=(1+sinθcosθ)(1−sinθ1),

=1−sin2θcosθ,

=cos2θcosθ,

=cosθ, as desired!


hope you like my answer sir plz mark as brainlist if ihas correct

Answer 2

I'm replacing theta by A for convenience.

L.H.S = sec A + tan A
= 1/cos A + sin A/cos A
= (1 + sin A)/cos A
= (1 + sin A)(1 - sin A)/cos A (1 - sin A)
= (1 - sin² A)/ cos A (1 - sin A)
= (cos ² A)/cos A (1 - sin A)
= cos A/1 - sin A = RHS.

Q.E.D.