Question

2cotA = 4/2 prove 1-tan²A/1+tan² A= cos²A- sin²A​

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}}$

$2cotA = \frac{4}{2}$

$cotA = \frac{4}{4}$

$cotA =1$

$cotA = \frac{\pi}{4}$

SO

$tan A = tan \frac{\pi}{4} = 1$

LHS

$\frac{1-tan²A}{1+tan² A} = \frac{1 - 1}{1 + 1} = 0$

RHS

$cos²A- sin²A = cos² \frac{\pi}{4} - sin² \frac{\pi}{4} = \frac{1}{2} - \frac{1}{2} = 0$

So LHS=RHS

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