Question

Prove that :-

cosA/1-tanA + sinA/1-cotA
= cosA + sinA​

Answer 1

Answer:

Step-by-step explanation:

= cosA/1-tanA + sinA/1-cotA

= cosA/1-sinA/cosA + sinA/1-cosA/sinA

= cos2 A/cosA – sinA – sin2 A/cosA – sinA

= cos2 A - sin2 A/ cosA – sinA

= (cosA + sinA)( cosA – sinA)/ cosA – sinA

= sinA + cosA

Hence proved..

Hope it will help you..

Answer 2

Step-by-step explanation:

★ Question :-

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⟶ Prove that :-

$\large \bold { \frac{cosA}{1 - tanA} + \frac{sinA}{1 - cotA} = cosA + sinA }$

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★ Answer :-

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⠀⠀$\bold\red{L.H.S} \bold{ \: = \frac{cosA}{1 - tanA } + \frac{sinA}{1 - cotA} } \\ \\ \bold{ = \frac{cosA}{1 - \frac{sinA}{cosA} } + \frac{sinA}{1 - \frac{cosA}{sinA} } } \\ \\ \bold{ = \frac{cosA}{ \frac{cosA - sinA}{cosA} } + \frac{sinA}{ \frac{sinA - cosA}{sinA} } } \\ \\ \bold{= \frac{cos {}^{2}A }{cosA - sinA} + \frac{sin {}^{2} A}{sinA - cosA} } \\ \\ \bold{ = \frac{cos {}^{2} A}{cosA - sinA} - \frac{sin {}^{2}A }{cosA - sinA} } \\ \\ \bold{ = \frac{cos {}^{2}A - sin {}^{2} A}{cosA - sinA} } \\ \\ \bold{ = \frac{(cosA - sinA)(cosA + sinA)}{cosA - sinA} } \\ \\ \fbox \pink{ = cosA + sinA} \bold \red{ \: \: \: \: \: \: \: =R.H.S }$

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$\green{ \fcolorbox{gray}{black} {\textbf{ Hence, Proved ✔ }}}$

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$\large\colorbox{pink}{Hope lt'z Help You ❥ }$