Question

Prove it:-
(1 + cos A + cos2A)÷
(sin A + sin2A) =cotA
Class -XI-sc​

Answer 1

TO PROVE :-

$\sf \dfrac{1+cosA+cos2A}{sinA+sin2A}= cotA$

SOLUTION :-

$\sf L.H.S = \dfrac{1+cosA+cos2A}{sinA+sin2A}$

We know that,

$\bullet\bf \ cos2A= 2cos^2-1 \\\\\bullet\bf \ sin2A= 2sinAcosA$

         $= \sf \dfrac{1+cosA+2cos^2A-1}{sinA+2sinAcosA} \\\\= \dfrac{cosA+2cos^2A}{sinA+2sinAcosA}$

Taking $\sf cosA$ and $\sf sinA$ as common,

        $= \sf \dfrac{cosA(1+2cosA)}{sinA(1+2cosA)} \\\\= \dfrac{cosA}{sinA} \\\\= cotA \\\\= R.H.S$

Hence proved.