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CGP EDU Academic Team
Published on: August 14, 2026
If cos − 1 x + cos − 1 y + cos − 1 z = π , where − 1 ≤ x, y, z ≤ 1, then find the value of x 2 + y 2 + z 2 + 2 x y z
Text Solution
Verified by ExpertsThe correct answer is:
1
(1)
Sol. cos –1 x + cos –1 y + cos –1 z = π
– 1 ≤ x, y, z ≤ 1
let x = cos A, y = cos B, z = cos C
where 0 ≤ A, B, C ≤ π
A + B + C = π
x 2 + y 2 + z 2 + 2xyz = cos 2 A + cos 2 B + cos 2 C + 2 cos A cos B cos C
= 
+ 2 cos A cos B cos C
= 
+ 
(–1 – 4 cos A cos B cos C) + 2 cos A cos B cos C = 1
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