If a line in the space makes angle α, β and γ with the coordinate axes, then cos 2 α+cos 2 β+cos 2 γ+sin^2 α+ sin^2 β + sin^2 γ equals

Correct answer: (C) 1. cos 2 α+cos 2 β+cos 2 γ +sin^2 α+sin^2 β+sin^2 γ (cos^2 α-sin^2 α )+ (cos^2 β-sin^2 β ) (cos^2 γ-sin^2 γ )+sin^2 α+sin^2 β+sin^2 γ =cos^2 α+cos^2 β+cos^2 γ=1

Q68 / 120 · VITEEE 2009 · Mathematics

If a line in the space makes angle $\alpha, \beta$ and $\gamma$ with the coordinate axes, then $\begin{aligned} \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^{2} \alpha+& \sin ^{2} \beta \\ +& \sin ^{2} \gamma \text { equals } \end{aligned}$

A
$-1$
B
0
Correct answer
C
1
D
2

Solution

$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma$ $\quad+\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$ $\quad\left(\cos ^{2} \alpha-\sin ^{2} \alpha\right)+\left(\cos ^{2} \beta-\sin ^{2} \beta\right)$ $\quad\left(\cos ^{2} \gamma-\sin ^{2} \gamma\right)+\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$ $=\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1$

Hence, the correct answer is option: 'C'.

If a line in the space makes angle $\alpha, \beta$ and $\gamma$ with the coordinate axes, then $\begin{aligned} \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^{2} \alpha+& \sin ^{2} \beta \\ +& \sin ^{2} \gamma \text { equals } \end{aligned}$

Solution

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