1.

If `theta` is an acute angle such that `sec^2 theta=3`, then the value of `(tan^2 theta-cosec^2 theta)/(tan^2 theta+cosec^2 theta)` is

Answer» `sec^2 theta = 3`
`:. cos^2theta = 1/3 => cos theta = 1/sqrt3`
`:. sin^2theta = 1- cos^2theta = 1-1/3 = 2/3`
`:. tan^2theta = sin^2theta/cos^2theta = 2`
`cosec^2theta = 1/sin^2theta = 3/2`
`:. (tan^2theta-cosec^2theta)/(tan^2theta+cosec^2theta) =(2-3/2)/(2+3/2) = (1/2)/(7/2) = 1/7 `


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