Question

sin 5x - 2 sin 3x + sin x
cos5x - cos x
tan x​

Answer 1

Answer:

sinC−sinD=2cos(

2

C+D

)sin(

2

C−D

)

cosC−cosD=−2sin(

2

C+D

)sin(

2

C−D

)

LHS=

cos5x−cosx

sin5x−2sin3x+sinx

=

cos5x−cosx

(sin5x−sin3x)−(sin3x−sinx)

=

−2sin3xsin2x

2cos4xsinx−2cos2xsinx

=

−2sin3xsin2x

2sinx(cos4x−cos2x)

=

−2sin3x(2sinxcosx)

2sinx(−2sin3xsinx)

=

cosx

sinx

=tanx=RHS

LHS=RHS