1.

Consider equation (x - sin alpha) (x-cos alpha) - 2 = 0 . Which of the followingis /are true?

Answer»

If `0lt alpha LT (pi)/(4)`, then the equationhas both ROOTS in `(sin alpha, cos alpha)`
If `(pi)/(4) lt alpha (pi)/(2)`, then theequations has both rootsin `(sin alpha, cos alpha OO)`
If `0lt alpha lt (pi)/(4)`, theone roots lies in `(-oo, sin alpha)` and theotherin `(sin alpha,oo)`
If `(pi)/(4) lt alpha lt (pi)/(2)` thenone rootliesin `(-oo, cos alpha )` and the otheris `(sin alpha, oo)`

Solution :Let , `f(x) = (x - sin alpha ) (x - cos alpha) - 2 `
Then. ` f(sin alpha) = - 2 lt 0 ` and
` f(cos alpha) = - 2 lt 0 ` and
` f(cos alpha ) = - 2 lt 0 `
So, sin ` ALPHAAND cos alpha ` lie between the
roots



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