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प्रश्न
if `3 cos theta = 1`, find the value of `(6 sin^2 theta + tan^2 theta)/(4 cos theta)`
उत्तर
Given `3 cos theta = 1`
We have to find the value of the expression `(6 sin^2 theta + tan^2 theta)/(4 cos theta)`
We have
`3 cos theta = 1`
`=> cos theta = 1/3`
`sin theta = sqrt(1 - cos^2 theta) = sqrt(1- (1/3)^3) = sqrt8/3`
`tan theta = sin theta/cos theta = (sqrt8/3)/(1/3) = sqrt8`
Therefore,
`(6 sin^2 theta + tan^2 theta)/(4 cos theta) = (6 xx (sqrt8/3)^2 + (sqrt8)^2)/(4 xx 1/3)`
= 10
Hence, the value of the expression is 10.
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