Question

Prove that :sinA/1-cosA + tanA/1+cosA=secA.cosecA + cotA

Please answer it brainly experts
40 points!!!!

Answer 1

L.H.S

SIN A /1-COS A + TAN A / 1+ COS A

SIN(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^2A

1/SIN A +COS A / SIN A + 1/COS A + SIN A -1/SIN A

COS A / SIN A +1/ COS A .SIN A

COT A + SEC A . COSEC A = RHS

HENCE PROVED

Answer 2

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