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If p = a sin x + b cos x and q = a cos x - b sin x, then what is the of \( \Large p ^{2}+q^{2} \) ?
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A) a + b |
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B) ab |
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C) \( \Large a ^{2}+b^{2} \) |
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D) \( \Large a ^{2}-b^{2} \) |
Correct Answer:
| C) \( \Large a ^{2}+b^{2} \) |
Description for Correct answer:
Given, p = asin x + bcos x ...(i)
and q = acos x - bsin x ....(ii)
On squaring both the equations
\( \Large p^{2}=a^{2}sin^{2}x+b^{2}cos^{2}x \)+2ab sinx cosx
and \( \Large q^{2}=a^{2}cos^{2}x+b^{2}sin^{2}x \)-2ab sinx cosx
\( \Large p^{2}+q^{2}=a^{2}sin^{2}x+b^{2}cos^{2}x \)
\( \Large +2ab \ sinx \ cosx
+a^{2} \ cos^{2}x+b^{2}sin^{2}x-2ab \ sinx \ cosx \)
\( \Large p^{2}+q^{2}=a^{2}(sin^{2}x+cos^{2}x)\)
\(+b^{2}(cos^{2}x+sin^{2}x) \)
= \( \Large a^{2}+b^{2} \)
Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry
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