Question

Question 15 Prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

LHS = cot4x(sin5x + sin3x)
Use the formula,
sinC + sinD = 2sin(C + D)/2.cos(C-D)/2

= cot4x {2sin(5x+3x)/2.cos(5x-3x)/2}
=cot4x(2sin4x.cos2x)
=cos4x/sin4x ( 2sin4x.cos2x)
= 2cos4x.cos2x
again,
RHS = cotx ( sin5x - sin3x)
Similarly , use the formula,
SinC - sinD = 2cos(C+D)/2.sin(C-D)/2

= cotx{2cos(5x+3x)/2.sin(5x-3x)/2}
= cosx/sinx(2cos4x.sinx)
= cosx .2cos4x
= cos4x.cosx

LHS = RHS