Question

Question 14 Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

LHS = sin2x + 2sin4x + sin6x
=(sin2x + sin6x) + 2sin4x
Now , use the formula,
sinC + sinD = 2sin(C+D)/2.cos(C-D)/2

= 2sin(2x+6x)/2.cos(6x -2x)/2+ 2sin4x
= 2sin4x.cos2x + 2sin4x
= 2sin4x ( cos2x + 1)

Now , use the formula,
cos2A + 1 = 2cos²A

= 2sin4x (2cos²x)
= 4cos²x.sin4x = RHS

Answer 2

here your answer in pic..