jee-main 2013 Q77

jee-main · India · 07apr Sine and Cosine Rules Multi-step composite figure problem

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC \perp CD$. If $\angle ADB = \theta$, $BC = p$ and $CD = q$, then $AB$ is equal to
(1) $\frac{p^2 + q^2}{p^2 \cos\theta + q^2 \sin\theta}$
(2) $\frac{\left(p^2 + q^2\right)\sin\theta}{(p\cos\theta + q\sin\theta)^2}$
(3) $\frac{\left(p^2 + q^2\right)\sin\theta}{p\cos\theta + q\sin\theta}$
(4) $\frac{p^2 + q^2\cos\theta}{p\cos\theta + q\sin\theta}$

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC \perp CD$. If $\angle ADB = \theta$, $BC = p$ and $CD = q$, then $AB$ is equal to\\
(1) $\frac{p^2 + q^2}{p^2 \cos\theta + q^2 \sin\theta}$\\
(2) $\frac{\left(p^2 + q^2\right)\sin\theta}{(p\cos\theta + q\sin\theta)^2}$\\
(3) $\frac{\left(p^2 + q^2\right)\sin\theta}{p\cos\theta + q\sin\theta}$\\
(4) $\frac{p^2 + q^2\cos\theta}{p\cos\theta + q\sin\theta}$

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