Test Index

SSC CHSL 8 Jan 2017 Shift 1 Paper

© examsnet.com

Question : 65 of 100

Marks: +1, -0

If sinC + sinD =X, then the value of X is?

2cos[(C+D)/2]sin[(C-D)/2]
2sin[(C+D)/2]cos[(C-D)/2]
2cos[(C+D)/2]cos[(C-D)/2]
2sin[(C+D)/2]sin[(D-C)/2]

Solution:

We know that,

\sin(x+y)=\sin x \cos y

+\cos x \sin y

--------(i)

and

\sin(x-y)=\sin x \cos y

-\cos x \sin y

--------(ii)

Adding equations (i) and (ii), we get :

\sin(x+y)+\sin(x-y)

=2\sin x \cos y

-----(iii)

Let

x+y=C

and

x-y=D

⇒

x=\frac{C+D}{2}

y=\frac{C-D}{2}

Substituting above values in equation (iii)

⇒

\sin C+\sin D =2\sin\left(\frac{C+D}{2}\right)

\cos\left(\frac{C-D}{2}\right)

© examsnet.com

Go to Question:

Prev Question

Next Question