Question

If 7cosecA-3cotA=7, prove that 7cotA-3CosecA=3

Answer 1

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Answer 2

Step-by-step explanation:

$7cosecA-3cotA=7$

$\implies \frac{7}{sinA}-3\frac{cosA}{sinA}=7$

$\implies \frac{7-3cosA}{sinA}=7$

$\implies 7-3cosA=7sinA$

$\implies 7-7sinA=3cosA$

$\implies 7(1-sinA)=3cosA$

$\implies \frac{7}{3}=\frac{cosA}{1-sinA}\\=\frac{cosA(1+sinA)}{(1-sinA)(1+sinA)}\\=\frac{cosA(1+sinA)}{1^{2}-sin^{2}A}\\=\frac{cosA(1+sinA)}{cos^{2}A}\\=\frac{1+sinA}{cosA}$

$\implies 7cosA=3(1+sinA)$

$\implies 7cosA=3+3sinA$

Divide each term by sinA ,we get

$\implies \frac{7cosA}{sinA}=\frac{3}{sinA}+\frac{3sinA}{sinA}$

$\implies 7cotA=3cosecA+3$

$\implies 7cotA-3cosecA=3$

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