Question
Very-Short and Short-Answer Questions.If $\text{x}=\text{a}\sin\theta$ and $\text{y}=\text{b}\cos\theta,$ write the value of $\Big(\text{b}^2\text{x}^2+\text{a}^2\text{y}^2\Big).$
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Answer
$\text{x}=\text{a}\sin\theta$ and $\text{y}=\text{b}\cos\theta$Now,
$=\text{b}^2(\text{a}\sin\theta)^2+\text{a}^2(\text{b}\cos\theta)^2$
$=\text{a}^2\text{b}^2\sin^2\theta+\text{a}^2\text{b}^2\cos^2\theta$
$=\text{a}^2\text{b}^2\big(\sin^2\theta+\cos^2\theta\big)$
$=\text{a}^2\text{b}^2\times1$
$=\text{a}^2\text{b}^2$
$=\text{b}^2(\text{a}\sin\theta)^2+\text{a}^2(\text{b}\cos\theta)^2$
$=\text{a}^2\text{b}^2\sin^2\theta+\text{a}^2\text{b}^2\cos^2\theta$
$=\text{a}^2\text{b}^2\big(\sin^2\theta+\cos^2\theta\big)$
$=\text{a}^2\text{b}^2\times1$
$=\text{a}^2\text{b}^2$
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