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Prove $: \tan \left(\frac{\pi}{4}+A\right)=\frac{\cos A+\sin A}{\cos A-\sin A}$

written 5.2 years ago by teamques10 ★ 68k

modified 2.6 years ago by pedsangini276 • 4.8k

engineering mathematics

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written 5.2 years ago by teamques10 ★ 68k

Solution:

$\tan \left(\frac{\pi}{4}+A\right)$

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

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

$=\frac{1+\tan A}{1-\tan A}$

$=\frac{1+\frac{\sin A}{\cos A}}{1-\frac{\sin A}{\cos A}}$

$=\frac{\cos A+\sin A}{\cos A-\sin A}$

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