Question

Cosec theta + cot theta = (2cosec theta cot theta) /root 2 cot theta

Answer 1

Answer:

cosecθ−cotθ=

2

cotθ

\implies cosec \theta = \sqrt{2} cot \theta + cot \theta⟹cosecθ=

2

cotθ+cotθ

\implies cosec \theta = cot \theta (\sqrt{2} + 1)⟹cosecθ=cotθ(

2

+1)

\implies \frac{cosec \theta }{\sqrt{2} + 1}=cot \theta⟹

2

+1

cosecθ

=cotθ

\implies \frac{cosec \theta \times (\sqrt{2} - 1)}{2 - 1}= cot \theta⟹

2−1

cosecθ×(

2

−1)

=cotθ

( By rationalizing )

\implies \frac{ \sqrt{2} cosec \theta - cosec \theta}{1}=cot \theta⟹

1

2

cosecθ−cosecθ

=cotθ

\implies \sqrt{2} cosec \theta - cosec \theta = cot\theta⟹

2

cosecθ−cosecθ=cotθ

\implies \sqrt{2} cosec \theta = cot\theta+cosec \theta⟹

2

cosecθ=cotθ+cosecθ

Hence, proved.