Question

(osA
/1 +sin A
)+(1+ inA
/cos A)
=

(A) 2CosecA
(B) 2 CosA

(C) 2 SecA
(D) 2 SinA​

Answer 1

Answer:

Hi !

Let us start with the LHS

LHS = 1 + cosA/sinA + sinA / 1+ cosA

here , LCM = sinA(1+ cosA)

= \frac{(1+cosA) ^{2} + (sinA) ^{2} }{sinA(1 + cosA)}=

sinA(1+cosA)

(1+cosA)

2

+(sinA)

2

= \frac{ 1 + 2cosA + co s^{2}A + sin ^{2}A }{sinA(1 + cosA)}=

sinA(1+cosA)

1+2cosA+cos

2

A+sin

2

A

We know that ,

sin²A + cos²A = 1

Hence,

= \frac{1 + 1 + 2 cosA}{sinA( 1 + cosA)}=

sinA(1+cosA)

1+1+2cosA

\frac{2 + 2 cosA}{sinA(1+cosA)}

sinA(1+cosA)

2+2cosA

= \frac{2 ( 1 + cosA)}{sinA(1+ cosA)}=

sinA(1+cosA)

2(1+cosA)

1 + cosA gets cancelled , ( in numerator and denominator).

= 2 / sinA

= 2* 1/sinA

We know that , 1/sinA = cosec A

Hence,

= 2*1/sinA = 2* cosecA = 2cosecA = RHS

PROVED.