Question

sin^8x - cos^8x = (sin^2x - cos^2x) (1-2sin^2x-cos^2x)
If you answer it properly. I will you mark you as brainliest...

Answer 1

L.H.S
sin
8
x−cos
8
x

⇒(sin
4
x)
2
−(cos
4
x)
2


⇒(sin
4
x−cos
4
x)(sin
4
x+cos
4
x) ∵(a
2
−b
2
)=(a−b)(a+b)

⇒((sin
2
x)
2
−(cos
2
x)
2
)((sin
2
x+cos
2
x)
2
−2sin
2
xcos
2
x) ∵(a+b)
2
−2ab=a
2
+b
2


⇒((sin
2
x−cos
2
x)(sin
2
x+cos
2
x))((sin
2
x+cos
2
x)
2
−2sin
2
xcos
2
x)

⇒((sin
2
x−cos
2
x)(1))((1)
2
−2sin
2
xcos
2
x) ∵sin
2
x+cos
2
x=1

=(sin
2
x−cos
2
x)(1−2sin
2
xcos
2
x)

R.H.S
Hence, proved.

Answer 2

Step-by-step explanation:

Basic trigonometric and algebraic identities can help you prove this question..