Question

Prove the identity:​

Answer 1

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Answer 2

Given expression :

• (Sec²A - Sin²A)/tan²A = Cosec²A - Cot²A

Taking LHS,

→ Sec²A × (1/Tan²A) - Sin²A × (1/tan²A)

We know that,

★ Sec²A = 1/Cos²A

★ 1/Tan²A = Cos²A/Sin²A

Putting the values,

→ (1/Cos²A) × (Cos²A/Sin²A) - Sin²A × (Cos²A/Sin²A)

Cancelling cos²A to cos²A and Sin²A to Sin²A

→ (1/sin²A) - cos²A

We also know that,

★ Cosec²A = 1/Sin²A

Putting the value,

→ Cosec²A - Cot²A

→ RHS

Hence proved!