AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\alpha+\beta=\gamma\), then what is the value of \(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma\) is equal to
- A \(1+2 \cos ^3 \alpha \cos ^3 \beta \cos ^3 \gamma\)
- B \(1+2 \cos ^2 \alpha \cos ^2 \beta \cos ^2 \gamma\)
- C \(1+2 \cos \alpha \cos \beta \cos \gamma\)
- D \(1+4 \cos \alpha \cos \beta \cos \gamma\)
Answer & Solution
Correct Answer
(C) \(1+2 \cos \alpha \cos \beta \cos \gamma\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } \alpha+\beta=\gamma \\ & \text { Then, } \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma \\ & =\frac{1}{2}\left[2 \cos ^2 \alpha+2 \cos ^2 \beta+2 \cos ^2 \gamma\right] \\ & \qquad=\frac{1}{2}\left[1+\cos 2 \alpha+1+\cos 2 \beta+2 \cos ^2…
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