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Question
If `cot theta = 1/ sqrt(3)`, write the value of `((1 - cos^2 theta))/((2 - sin^2 theta))`.
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Solution
We have,
`cot theta = 1/ sqrt(3)`
⇒ `cot theta = cot (π/3)`
⇒ `theta = π/3`
Now,
`((1- cos^2 theta))/((2 - sin^2 theta))`
= `(1- cos ^2(π/3))/( 2 - sin ^2 ( π/ 3))`
= `(1- (1/2)^2)/(2-(sqrt(3)/2)^2)`
= ` ((1/1 - 1/4))/((2/1-3/4))`
= `((3/4))/((5/4))`
= `3/5`
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