Question

(1+tan^2A)(1+cot^2A)=1/sin^2A-sin^4​

Answer 1

Answer:

Step-by-step explanation:

The answer won't be equal to RHSit 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.

Hope it helps.