Answer:
Given:
(sin5x−sinx)(cos4x−cos6x)
(cosx−cos3x)(sin8x+sin2x)
Use the formula:
sina+sinb=2sin(
2
a+b
)cos(
2
a−b
)
sina−sinb=2cos(
2
a+b
)sin(
2
a−b
)
cosa−cosb=−2sin(
2
a+b
)sin(
2
a−b
)
(sin5x−sinx)(cos4x−cos6x)
(cosx−cos3x)(sin8x+sin2x)
=
(2cos
2
6x
sin
2
4x
)(−2sin
2
10x
sin
2
−2x
)
(−2sin
2
4x
sin
2
−2x
)(2sin
2
10x
cos
2
6x
)
=
(2cos3xsin2x)(2sin5xsinx)
(2sin2xsinx)(2sin5xcos3x)
=1
