AP

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

If cos⁡−1x+cos⁡−1y+cos⁡−1z=π\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = \pi , then (1) x2+y2+z2+2xyz=1x^2 + y^2 + z^2 + 2xyz = 1 (2) 2(sin⁡−1x+sin⁡−1y+sin⁡−1z)=cos⁡−1x+cos⁡−1y+cos⁡−1z2(\sin^{-1} x + \sin^{-1} y + \sin^{-1} z) = \cos^{-1} x + \cos^{-1} y + \cos^{-1} z (3) xy+yz+zx=x+y+z−1xy + yz + zx = x + y + z - 1 (4) (x+1x)+(y+1y)+(z+1z)≥6\left(x + \frac{1}{x}\right) + \left(y + \frac{1}{y}\right) + \left(z + \frac{1}{z}\right) \ge 6

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