Question

If sin3a = 4sin a sin (x + a) sin (x – a),
then x =
(A) na
(B) NAHO
(C) n
(D)
+​

Answer 1

Step-by-step explanation:

sin3a = 4sin(a)sin(x+a)sin(x-a)

putting 3sin(a) - 4sin^3(a) in place of sin3a

sin(a)(3 - 4sin^2(a)) = 4sin(a)sin(x+a)sin(x-a)

3 - 4sin^2(a) = 4sin(x+a)sin(x-a)

as we know that

sin(c)sin(d)= 2sin(c+d/2)cos(c-d/2)

by using above formula

3 - 4sin^2(a)=4×2sin(x)cos(a)

3 - 4 + 4cos^2(a)=8sin(x)cos(a)

4cos^2(a) - 1=8sin(x)cos(a)

4cos(a) - sec(a)=8sinx

cos(a)/2 - sec(a)/8=sin(x)

arc sin(cos(a)/2 - sec(a)/8) = x