Question

cos⁡A/(1 - tan⁡A ) + sin⁡A/(1 -〖 cot〗⁡〖 A〗 ) = sin A + cos A

Answer 1

SOLUTION:-

Given:

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

To prove:

sinA + cosA

Proof:

Take L.H.S

$= > \frac{cosA}{cosA} - \frac{sinA}{cosA} + \frac{sinA}{sinA} - \frac{cosA}{sinA} \\ \\ = > \frac{ {cos}^{2} A}{cosA - sinA} - \frac{ {sin}^{2} A}{cosA - sinA} \\ \\ = > \frac{ {cos}^{2}A - {sin}^{2}A }{cosA- sinA} \\ \\ = > \frac{(cosA + sinA)(cosA - sinA)}{cosA - sinA} \\ \\ = > cosA + sinA \: \: \: \: \: \: \: \: \: [R.H.S.]$

Proved.

Answer 2

*。Important point

Here we have applied :-

→tan A = sinA/cosA

→cot A = cosA/sinA

→cos²A - sin²A = a² - b² i.e (a+b)(a-b)

And hence proved

hope it helps

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