Prove-that-sin-2cos-1-

Question Number 12378 by tawa last updated on 20/Apr/17

Prove that,

\sin θ + 2 \cos θ = 1

Commented by mrW1 last updated on 21/Apr/17

t h i s i s n o t t r u e .

θ = 0 \Rightarrow \sin θ + 2 \cos θ = 2 \neq 1

Commented by tawa last updated on 21/Apr/17

God bless you sir .

Answered by mrW1 last updated on 23/Apr/17

d o y o u m e a n t o s o l v e \sin θ + 2 \cos θ = 1 ?

\sqrt{5} (\frac{1}{\sqrt{5}} \sin θ + \frac{2}{\sqrt{5}} \cos θ) = 1

\sqrt{5} (\cos α \sin θ + \sin α \cos θ) = 1

w i t h α = \sin^{- 1} (\frac{2}{\sqrt{5})})

\sqrt{5} \sin (θ + α) = 1

\sin (θ + α) = \frac{1}{\sqrt{5}}

\Rightarrow θ + α = \sin^{- 1} (\frac{1}{\sqrt{5}})

\Rightarrow θ = \sin^{- 1} (\frac{1}{\sqrt{5}}) - \sin^{- 1} (\frac{2}{\sqrt{5}})

\sin θ = \frac{1}{\sqrt{5}} \times \frac{1}{\sqrt{5}} - \frac{2}{\sqrt{5}} \times \frac{2}{\sqrt{5}} = - \frac{3}{5}

\cos θ = \frac{4}{5}

\Rightarrow θ = - \sin^{- 1} (\frac{3}{5}) + 2 n π

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