Solve:cos−1(53cosx−4sinx )

Given,cos−1(53cosx−4sinx)=cos−1(53cosx−54sinx)Let 53=cosα,54=sinαTherefore,=cos−1(cosαcosx−sinαsinx)=cos−1(cos(x+α))=x+α where α=cos−153Hence, this is the answer.

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Solve: { }^{ -1 }( { 3 x-4 x }{ 5 } )

Question

Solve:
$cos^{- 1} (\frac{3 cos x - 4 sin x}{5})$

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Text solutionVerified

Given,

cos^{- 1} (\frac{3 cos x - 4 sin x}{5})

= cos^{- 1} (\frac{3}{5} cos x - \frac{4}{5} sin x)

Let

\frac{3}{5} = cos α, \frac{4}{5} = sin α

Therefore,

= cos^{- 1} (cos α cos x - sin α sin x)

= cos^{- 1} (cos (x + α))

= x + α

where

α = cos^{- 1} \frac{3}{5}

Hence, this is the answer.

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Question Text	Solve: $cos^{- 1} (\frac{3 cos x - 4 sin x}{5})$
Answer Type	Text solution:1
Upvotes	150

Solve:cos−1(53cosx−4sinx​ )

Text solutionVerified

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Solve:
$cos^{- 1} (\frac{3 cos x - 4 sin x}{5})$