Question

If sin theta = cos theta, find 2sin theta - cos theta​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:- sinθ+cosθ=

2

cosθ

To prove:- cosθ+sinθ=

2

sinθ

Proof:-

sinθ+cosθ=

2

cosθ

Squaring both sides, we get

sin

2

θ+cos

2

θ+2sinθcosθ=2cos

2

θ

⇒sin

2

θ−cos

2

θ+2sinθcosθ=0

Subtracting 2sin

2

θ both sides, we have

−sin

2

θ−cos

2

θ+2sinθcosθ=−2sin

2

θ

sin

2

θ+cos

2

θ−2sinθcosθ=2sin

2

θ

(cosθ−sinθ)

2

=2sin

2

θ

⇒cosθ−sinθ=

2

sinθ

Hence proved.