Question

prove that 8 sin⁴ ½theta-8 sin² ½ theta +1 = cos 2 theta​

Answer 1

Answer:

(sin

8

θ−cos

8

θ)=(sin

4

θ)

2

−(cos

4

θ)

2

=(sin

4

θ−cos

4

θ)(sin

4

θ+cos

4

θ)

⇒LHS=(sin

2

θ−cos

2

θ)(sin

2

θ+cos

2

θ)(sin

4

θ+cos

4

θ)

⇒LHS=(sin

2

θ−cos

2

θ)[(sin

2

θ)

2

+(cos

2

θ)

2

+2sin

2

θcos

2

θ−2sin

2

θcos

2

θ]

⇒LHS=(sin

2

θ−cos

2

θ)[(sin

2

θ+cos

2

θ)

2

−2sin

2

θcos

2

θ]

⇒LHS=(sin

2

θ−cos

2

θ)(1−2sin

2

θcos

2

θ)=RHS

Answer 2

Step-by-step explanation:

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