Question

sinx/sin(x/8)=?

options:
a) 0
b)1
c)8 cos x/8 cos x/4 cos x/2
d)8 sin x/8 sin x/4 sin x/2

Answer 1

the correct answer to this question would be option b

Answer 2

Answer:

Option C - 8 cos x/8 cos x/4 cos x/2

Step-by-step explanation:

Given : $\frac{sinx}{sin (x/8)}$

To find : the given statement is equal to

Solution : Using property of trigonometry

→ $Sin2x=2 sinx cosx$

Now,solve the given statement

$\frac{sinx}{sin (x/8)}$

$=\frac{2 sin(x/2) cos(x/2)}{sin (x/8)}$  ,  ∵ $[sinx=2 sin(x/2) cos(x/2)]$

$=\frac{2 cos(x/2) 2 sin(x/4) cos(x/4)}{sin (x/8)}$   ,  ∵$[sin(x/2)=2 sin(x/4) cos(x/4)]$

Further,

$=\frac{4 cos(x/2) cos(x/4) 2 sin(x/8) cos(x/8)}{sin (x/8)}$ ,    ∵$[sin(x/4)=2 sin(x/8) cos(x/8)]]$

$sin(x/8)$ cancel from numerator and denominator

$=8 cos(x/2) cos(x/4) cos(x/8)$  

Therefore, Option C is correct.