Question

Prove the identity:
secθ + cosecθ x cotθ = secθ x (cosecθ)^2

Answer 1

Answer:

$\huge\colorbox{orange}{ANSWER}$

Now,

(cosecθ−sinθ)(secθ−cosθ)

=(sinθ1−sinθ)(cosθ1−cosθ)

=(sinθ1−sin2θ)(cosθ1−cos2θ)

=sinθcosθcos2θsin2θ=sinθcosθ                  (1)

Next, consider tanθ+cotθ1

=cosθsinθ+sinθcosθ1

=(sinθcosθsin2θ+cos2θ)1

=sinθcosθ                (2)

From (1) and (2), we get

(cosecθ−sinθ)(secθ−cosθ)=tanθ+cotθ