Thread: identities

Hi Guys would be grateful for some help on this question

Find in exact form, all roots of the equation 2sin²x + cosec²x = 3 which lies between 0 and 360 degrees.

thankyou

Originally Posted by gracey

Hi Guys would be grateful for some help on this question

Find in exact form, all roots of the equation 2sin²x + cosec²x = 3 which lies between 0 and 360 degrees.

thankyou

First replace sin x with w, say. Then you have 2 w^2 + 1/w^2 = 3 => 2w^4 + 1 = 3w^2 => 2w^4 - 3w^2 + 1 = 0 => (2w^2 - 1)(w^2 - 1) = 0.

Solve for w (four solutions). Use those values to solve the four different equations sin x = w (one equation for each value of w) ....