Question

prove sin2 a + 1/1+tan2a =1

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

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Sin²A + 1/1+tan²A

Sin²A + 1/sec²A (1+tan²A = sec²A)

Sin²A + Cos²A (1/secA = cosA)

Sin²A + Cos²A = 1. (By Identity)

HENCE PROVED

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