How do you prove 1 + cot2 x = csc2 x?

We have to prove 1 + cot2x = csc2x

Solution

Let us start with LHS

1 + cot2x

Expressing the given expression in terms of sin and cos

\(\frac{sin^{2}x}{\sin ^{2}x} + \frac{cos^{2}x}{\sin ^{2}x}\)

=\(\frac{cos^{2}x + sin^{2}x}{\sin ^{2}x}\)

= \(\frac{1}{\sin ^{2}x}= csc^{2}x\)

= RHS

Hence Proved

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