Question

prove that : .cosA/1-tanA +sinA/1-cotA=sinA+cosA​

Answer 1

Answer:

Your answer attacted in the photo

Answer 2

To Prove:

$\bf{\dfrac{cosA}{1-tanA}+\dfrac{sinA}{1-sinA}=sinA + cosA}$

Solution:

tan A can be written as sin A by cos A

$\sf{\dfrac{cosA}{1-\dfrac{sinA}{cosA}}+\dfrac{sinA}{1-\dfrac{cosA}{sinA}}}$

$= \: \sf{\dfrac{cosA}{\dfrac{cosA-sinA}{cosA}}+\dfrac{sinA}{\dfrac{sinA-cosA}{sinA}}}$

$= \: \sf{\dfrac{cos^{2} A}{cosA-sinA}+\dfrac{sin^{2}A}{sinA-cosA}}$

$= \: \sf{\dfrac{cos^{2}A}{cosA-sinA}-\dfrac{sin^{2}A}{cosA-sinA}}$

$= \: \sf{\dfrac{cos^{2}A-sin^{2}A}{cosA-sinA}}$

$= \: \sf{\dfrac{(cosA+sinA)(cosA-sinA)}{(cosA-sinA)}}$

$= \: \sf{sinA+cosA}$

$\green{\star} \: \pink{\underline{\sf{HENCE \: PROVED}}} \: \green{\star}$