Question

Tan²theta-cot²theta=sec²theta(1-cot²theta)

Answer 1

Step-by-step explanation:

tan²θ-cot²θ

=sec²θ-1-cosec²θ+1

=sec²θ-cosec²θ

=sec²θ(1-cos²θ/sin²θ)

=sec²θ(1-cot²θ)

Answer 2

Given,

LHS=tan²Φ-cot²Φ

RHS=sec²Φ(1-cot²Φ)

LHS

=tan²Φ-cot²Φ

=sec²Φ-1-cosec²Φ+1

=sec²Φ-cosec²Φ

=sec²Φ(1-cot²Φ)

LHS=RHS

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