Question

Prove this.......
Urgent!!!!​

Answer 1

LHS ,

= (1+cot²A)(1+tan²A)

= cosec²A × sec²A

= 1/sin²A × 1/cos² A

= 1/sin²A × 1/(1-sin²A)

= 1/sin²A - sin⁴A.

= RHS.

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Answer 2

Hence it is proved that ( 1 + 1/tan²A ) ( 1 + 1/cot²A ) = 1/( sin²A - sin^4A )

To prove,

( 1 + 1/tan²A ) ( 1 + 1/cot²A ) = 1/( sin²A - sin^4A )

LHS:

= ( 1 + 1/tan²A ) ( 1 + 1/cot²A )

wkt tanA = 1/cotA and vice versa

= ( 1 + cot²A ) ( 1 + tan²A )

= cosec²A × sec²A

= 1/sin²A × 1/cos²A

wkt cos²A + sin²A = 1

= 1/sin²A × 1/(1-sin²A)

= 1/sin²A(1-sin²A)

= 1/( sin²A - sin^4A )

:RHS