Question

Prove the following trigonometric identities:

sin² A cot²A + cos²A tan²A =1

Answer 1

Given : sin² A cot²A + cos²A tan²A =1

To prove : Above equality holds. Proof: Consider LHS, we know,

cot θ =  \(\frac{cosθ}{sinθ}\)   and  tanθ = \(\frac{sinθ}{cosθ}\)

using these  

sin²A cot²A + cos²A tan²A

= sin²A x \(\frac{cos^2A}{sin^2A}\)  + cos²x \(\frac{sin^2A}{cos^2A}\)  

= cos²A sin²A

= 1

Which is equal to RHS. 

Hence Proved