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asked ago in Trigonometry by (7.1k points)

If cos-1x + cos-1y +cos-1z = p, then prove that x2 + y2 + z2 + 2xyz = 1.

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Given, cos-1x + cos-1y + cos-1z = π

⇒ cos-1x + cos-1y = π - cos-1z = cos-1(-z)

⇒ cos[cos-1x + cos-1y] = cos[cos-1(-z)]

Let cos-1x = A and cos-1y = B.

Then cos(A + B) = cosA cosB - sinA sinB

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