Question

please solve this question

step by step exaplanation!!

Answer 1

Answer:

clearly Lhs:

tan^2 x +cot^2 x + 2

= ( tan x + cot x )^2

= ( sinx/cos +cosx/ sin x)^2

= (1/cosx.sinx) ^2

= sec^2x.cosec^2x

=Rhs

Answer 2

L.H.S.

=> sin² x/cos²x + cos²x/sin²x + 2

L.C.M. = sin²x.cos²x

=> (sin⁴x + cos⁴x + 2sin²x.cos²x) ÷ sin²x.cos²x

=> [(sin²x)² + (cos²x)² + 2sin²x.cos²x] ÷ sin²x.cos²x

since a²+b²+2ab = (a+b)²

=> [sin²x + cos²x]² ÷ sin²x.cos²x

sin²x + cos²x = 1

=> 1 ÷ sin²x.cos²x

=> sec²x.cosec²x = R.H.S.