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If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ. - Mathematics

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If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.

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Solution

We have

α=90° 

β=60°

γ=θ

Since cos2α+cos2β+cos2γ=1,


`cos^2(90°)+cos^2(60°)+cos^2θ=1  `

`0^2+(1/2)^2+cos^2θ=1`

`cos^2θ=1−1/4=3/4`

`cosθ=sqrt3/2                    (θ is acute.)`

`∴ θ=30°`

Concept: Properties of Inverse Trigonometric Functions
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