Question

(cos teta+sin teta/cos teta-sin teta) - (cos teta-sin teta/cos teta+sin teta) =​

Answer 1

Answer:

Step-by-step explanation:

given equation is $\frac{cos x+ sin x}{cos x - sin x} -\frac{cos x - sin x}{cos x + sin x}$

taking LCM we get $\frac{(cos x + sin x)*(cos x + sin x) - (cos x - sinx )*(cos x - sin x)}{(cos x - sin x)*(cos +sin x)}$

=$\frac{(cos x + sin x)^{2} - (cos x - sin x)^{2}}{cos^{2}x - sin^{2}x}$

=$\frac{cos ^{2}x+sin^{2}x+2cos x sin x- cos^{2}x-sin^{2} x +2 cos x sinx}{cos 2x}$       since cos²∅-sin²∅=cos2∅

   = $\frac{4 cos x sin x}{cos 2x}$

= $\frac{2 sin2x}{cos 2x}$                          since 2sin∅cos∅ = sin 2∅

= 2 tan2x