Prove that : (cosec(90° + x) + cot(450° + x))/(cosec(90° + x) + tan(180° - x)) + (tan(180° + x) + sec(180° - x)/tan(360° + x)- sec(-x)) = 2

Question

Prove that :

\(\cfrac{cosec(90° + \text x) + cot(450°+\text x)}{cosec(90°+\text x)+tan(180° - \text x)}\) + \(\cfrac{tan(180° + \text x)+sec(180° - \text x)}{tan(360° + \text x)- sec(-\text x)}\) = 2

Answer 1

LHS =  \(\cfrac{cosec(90° + \text x) + cot(450°+\text x)}{cosec(90°+\text x)+tan(180° - \text x)}\) + \(\cfrac{tan(180° + \text x)+sec(180° - \text x)}{tan(360° + \text x)- sec(-\text x)}\) 

We know that when n is odd, cosec → sec and also sec (-x) = sec x.

= 1 + 1

= 2

= RHS

Hence proved.