Question

Prove the following trigonometric identities:
(1+tan²A)+(1+1/tan²A)=1/sin²A-sin4A

Answer 1

Step-by-step explanation:

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Answer 2

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

Step-by-step explanation:

To prove: (1 + tan²A) + (1 + 1/tan²A) = 1 / sin²A - sin^4 A

Proof:  

LHS (1 + tan²A) + (1 + 1/tan²A) = (1 + sin²A/cos²A) + (1 + 1/(sin²A/cos²A))

 = (cos²A + sin²A)/cos²A + (cos²A + sin²A)/sin²A

 = 1/cos²A + 1/sin²A  

 = 1/cos²A.sin²A  

 = 1/ [(1 - sin²A) sin²A]

= 1/ (sin²A - Sin^4 A)

LHS = RHS

Hence proved.