Question

solve this trigonometry​

Answer 1

Answer:

LHS

let us take 'theta' as 'x'

=(1+tan²x)+(1+1/tan²x)

=2+(tan²x)+(1/tan²x)

=2+(sin²x/cos²x)+(cos²x/sin²x)

=2+(sin⁴x+cos⁴x/sin²xcos²x)

=2sin²xcos²x+(sin²x)²+(cos²x)²/sin²xcos²x

(a+b)²=a²+b²+2ab

=(sin²x+cos²x)²/sin²xcos²x

sin²x+cos²x=1

=1/sin²xcos²x

cos²x=1-sin²x

=1/[sin²x(1-sin²x)]

=1/[sin²x-sin⁴x]

=RHS

Hence the proved

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