sinx+cosx=65\sin x + \cos x = \frac{6}{5}sinx+cosx=56 (sinx+cosx)2=3625sin2x+2sinxcosx+cos2x=36252sinxcosx=3625−1=1125(\sin x + \cos x)^2 = \frac{36}{25} \qquad \sin^2 x + 2\sin x \cos x + \cos^2 x = \frac{36}{25} \qquad 2\sin x \cos x = \frac{36}{25} - 1 = \frac{11}{25}(sinx+cosx)2=2536sin2x+2sinxcosx+cos2x=25362sinxcosx=2536−1=2511 sin2x=2sinx⋅cosx=1125\sin 2x = 2\sin x \cdot \cos x = \frac{11}{25}sin2x=2sinx⋅cosx=2511