Question

(1+ 1/tan^2A) (1+1/cot^2A) = (1+tan^2A) (1+cot^2A)= 1/sin^2A- sin^4 A)​

Answer 1

Step-by-step explanation:

(1+ 1/tan^2A) (1+1/cot^2A)= 1+tan^2A) (1+cot^2A)= 1/(sin^2A- sin^4 A)

LHS:

(1+ 1/tan^2A) (1+1/cot^2A)

= (1+cot^2A) (1+tan^2A)

= cosec²A•sec²A

= 1/sin²A • 1/cos²A

= 1/sin²A • 1/(1-sin²A)

= 1/(sin²A)(1-sin²A)

= 1/sin^2A- sin^4 A

so LHS=RHS=1/sin^2A- sin^4 A

HENCE PROVED....

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