Question

of sin theta +cos theta =a,then find the value of sin6 theta +cos 6 theta​

Answer 1

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11th

Maths

Trigonometric Functions

Trigonometric Equations

If sin theta + cos theta ...

MATHS

If sinθ + cosθ = x, prove that sin

6

θ+cos

6

θ=

4

4−3(x

2

−1)

2

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ANSWER

sinθ+cosθ=x

⇒sin

2

θ+cos

2

θ+2sinθcosθ=x

⇒1+2sinθcosθ=x

⇒sinθcosθ=(x−

2

1

)

sin

6

θ+cos

6

θ=(sin

2

θ)

3

+(cos

2

θ)

3

=(sin

2

θ+cos

2

θ)(sin

4

θ+cos

4

θ−sin

2

θcos

2

θ)

=((sin

2

θ+cos

2

θ)

2

−2sin

2

θcos

2

θ−sin

2

θcos

2

θ)=1−3sin

2

θcos

2

θ

=1−

4

3(x−1)

2

=

4

4−3(x−1)

2

.