Question

1+ sin2 theta+cos2 theta÷1+sin2 theta- cos theta = cot theta

Answer 1

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Answer 2

Answer and Explanation:

To prove : $\frac{1+ \sin 2\theta+\cos2\theta}{1+\sin 2\theta- \cos 2\theta} = \cot \theta$

Solution :

Taking LHS,

$\frac{1+ \sin 2\theta+\cos2\theta}{1+\sin 2\theta- \cos 2\theta}$

$=\frac{(1+\cos2\theta)+\sin 2\theta}{(1-\cos 2\theta)+\sin 2\theta}$

$=\frac{2\cos^2\theta+2\sin\theta\cos\theta}{2\sin^2\theta+2\sin\theta\cos\theta}$

$=\frac{2\cos\theta(\cos\theta+\sin\theta)}{2\sin\theta(\sin\theta+\cos\theta)}$

$=\frac{\cos\theta}{\sin\theta}$

$=\cot\theta$

= RHS

Hence proved.