Question

solve this question immediately​

Answer 1

Solution :-

We need to prove

(1 + 1/tan²A)(1 + 1/cot²A) = 1/(cos²A - cos⁴A)

Firstly taking LHS & simplifying

→ [ ( 1 + tan²A )/tan²A ] [ ( 1 + cot²A )/cot²A ]

As we know that

• 1 + tan²A = sec²A

• 1 + cot²A = cosec²A

→ [ sec²A/tan²A ] [ cosec²A/cot²A ]

Substituting

• sec²A = 1/cos²A

• tan²A = sin²A/cos²A

• cosec²A = 1/sin²A

• cot²A = cos²A/sin²A

→ [ ( 1/cos²A )/( sin²A/cos²A ) ] [ ( 1/sin²A )/( cos²A/sin²A ) ]

→ ( 1/sin²A ) ( 1/cos²A )

→ 1/sin²A cos²A

Now , substituting

• sin²A = 1 - cos²A

→ 1/( 1 - cos²A )cos²A

→ 1/cos²A - cos⁴A

Now , comparing with RHS

LHS = RHS

Hence , proved !