Trigonometry - Identities

If tan 2x = - 24/7, where 90 degrees < x < 180 degrees, then find the value of sin x+ cos x.
I applied various identities and tried manipulating the problem to get sin x + cos x = sin(arctan(-24/7)/2) + cos(arctan(-24/7)/2)
I also played around with the half-angle formula and the double angle formula but they both don't seem to work. Help would be appreciated, thanks.

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  1. 2θ is in QIV, so θ is in QII, and we have
    y = -24
    x = 7
    r = 25

    sin2θ = y/r = -24/25
    cos2θ = /r = 7/25

    now just apply the half-angle formulas and the identity should fall right out

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  2. Thanksa lot

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