Question

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

Answer:

The answer won't be equal to RHS 

it will be equal if  the question is:

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

LHS 

= (1 + 1/tan²A)(1 + 1/cot²A) 

= ((tan²A+1)/tan²A)((cot²A+1)/cot²A) 

= (sec²A/tan²A)(csc²A/cot²A) 

= (sec²A.csc²A)/(tan²A.cot²A) 

= sec²A.csc²A 

= 1/(sin²A.cos²A) 

= (1/sin²A)(1/cos²A) 

= (1/sin²A)(1/(1-sin²A)) 

= 1/(sin²A - sin^4.A) 

= RHS

hopefully it will help you...✌✌