Question

prove that 1+sin2theta-cos2theta/1+sin2theta+cos2theta=tantheta

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Answer 1

Given:

$\dashrightarrow\pink{ \boxed{\sf{\sf1+sin \: 2 \: theta-cos \: 2 \: theta}}}$

To Prove:

$\longmapsto \sf\frac{1+ \sin 2\theta+\cos2\theta}{1+\sin 2\theta- \cos 2\theta} = \sf \cot \theta$

Solution:

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

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

$\dashrightarrow\red{ \boxed{\sf{\frac{\cos\theta}{ \: \: \: \: \: \sin\theta \: \: \: \: \: }}}}$

$➝ \: \cot\theta$

• RHS

Hence Proved:

$\\{ \underline{ \rule{300pt}{9pt}}}$