Question

SinA/ 1-CosA +TanA/ 1+CosA= SecA×CosecA+CotA ​

Answer 1

$\large\bf{\underline\orange{Answer \:↝}}$

L.H.S

Sin A(1+ cos A)+tan A(1- cos A)/1- cos^2 A

Sin A + Sin A. cos A +tan A -tan A.cos A/sin^2 A

Sin A +Sin A. Cos A+tan A - sinA /Cos A + cos A/sin^2 A

Sin A +Sin A.cos A + tan A-Sin A/Sin^2 A

Sin A. cos A +sin A/Cos A/sin^2 A

Sin A(cos^2 A +1/cos A)/sin^2 A

Cos^2 A+1/cos A. sinA

Cos^2 A/cos A. SinA +1/cos A. sinA

cos A/Sin A +Sec A.Cosec A

Cot A + Sec A .Cosec A = RHS

hence proved.

Answer 2

Step-by-step explanation:

L.H.S

SinA/1-CosA + tanA / 1+ cos A

sinA /1- cos A + sin a / cosA(1+ cos A)

{SinA cos A (1+cosA) + sinA(1-cosA) } / cos A (1- cosA) (1+ cos A )

{sinAcosA + sinAcos^2A + sin A - sinAcosA}/ cosA(1-cos^2A )

sinAcos^2A + sinA / cosA sin^2A

sinAcos^2A/ cosA sin^2A + sinA/ cosA sin^2A

cosA/sinA + 1/ cosA sinA

cotA + secA cosecA. ( cosA/sinA = cotA) we know

so.

secA cosecA + cotA

HENCE RHS PROVED .

IF YOU UNDERSTAND THEN PLEASE MARK ME BRAINTLEST