Question

Prove that tan A×sin A/tan A+sin A=tan A-sin A/tan A×sin A

Answer 1

Proving:

Step-by-step explanation:

$\ Given \ value:\\\\\tan A \times \frac {\sin A}{\tan A} \ + \sin A \ = \tan A \ - \frac{\sin A}{\tan A} \times \sin A\\\\ \ Solution: \\\\\tan A \times \frac {\sin A}{\tan A} \ + \sin A \ = \tan A \ - \frac{\sin A}{\tan A} \times \sin A\\\\\ L.H.S: \\\\\tan A \times \frac {\sin A}{\tan A} \ + \sin A \\\\\rightarrow \sin A+ \sin A\\\\\rightarrow \ 2 \sin A \\\\\ R.H.S \\\\\tan A \ - \frac{\sin A}{\tan A} \times \sin A$

$\rightarrow \tan A \ - \frac{\sin A \cos A}{\sin A} \times \sin A\\\\\rightarrow \frac{\sin A}{\cos A} \ - \cos A \sin A\\\\\rightarrow \frac{\sin A- \cos^2 A \sin A}{\cos A}\\\\\rightarrow \frac{\sin A(\ 1 - \cos^2 A) }{\cos A}\\\\\rightarrow \tan A \sin^2 A$

L.H.S $\neq$ R.H.S

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• Proving: https://brainly.in/question/8112701