Question

prove it............​

Answer 1

Step-by-step explanation:

$\frac{1 + \cos(a) }{ \sin(a) } + \frac{ \sin(a) }{1 + \cos(a) }$

$\frac{ {(1 + \cos(a)) }^{2} + { \sin}^{2}(a) }{ \sin(a) (1 + \cos(a) )}$

taking only numerator

1+cos²a+2cosa+sin²a

1+1+2cosa(sin²a+cos²a)

2+2cosa

2(1+cosa)

now if we divide it with denominator (sinA)(1+cosa)

(1+cosa) will be cancel out from both side

only 2/sinA will be left which is equal to cosecA

Answer 2

LHS= (1+CosA)/SinA + SinA/(1+CosA)

=(1+CosA)^2+(SinA)^2÷ SinA(1+CosA)

=[1+2CosA+Cos^2A+Sin^2A] /SinA(1+CosA)

=[2+2CosA]/SinA(1+CosA)

=2(1+CosA) / SinA(1+CosA)

=2/SinA

=2CosecA

LHS=RHS. proved