व्यंजक $[ \frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}} + \sin^2 63 \cos 63^o \sin 27^o]$ का मान है
Exercise-8.1-11
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दिया गया है: $\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}} + \sin^2 63^o + \cos 63^o \sin 27^o$
$= \frac{\sin ^{2} 22^{\circ}+\sin ^{2}\left(90^{\circ}-22^{\circ}\right)}{\cos ^{2} 22^{\circ}+\cos ^{2}\left(90^{\circ}-22^{\circ}\right)} + \sin^2 63^o + \cos 63^o \sin (90^o - 63^o)$
$= \frac{\sin ^{2} 22^{\circ}+\cos ^{2} 22^{\circ}}{\cos ^{2} 22^{\circ}+\sin ^{2} 22^{\circ}} + \sin^2 63^o + \cos 63^o \cos 63^o...(\because \cos (90^o - \theta) = \sin \theta$ and $\sin (90^o - \theta) = \cos \theta)$
$\Rightarrow \frac{\sin ^{2} 22^{\circ}+\cos ^{2} 22^{\circ}}{\cos ^{2} 22^{\circ}+\sin ^{2} 22^{\circ}} + \sin^2 63^o + \cos^2 63^o$
$\Rightarrow \frac{1}{1} + 1 = 2$
$= \frac{\sin ^{2} 22^{\circ}+\sin ^{2}\left(90^{\circ}-22^{\circ}\right)}{\cos ^{2} 22^{\circ}+\cos ^{2}\left(90^{\circ}-22^{\circ}\right)} + \sin^2 63^o + \cos 63^o \sin (90^o - 63^o)$
$= \frac{\sin ^{2} 22^{\circ}+\cos ^{2} 22^{\circ}}{\cos ^{2} 22^{\circ}+\sin ^{2} 22^{\circ}} + \sin^2 63^o + \cos 63^o \cos 63^o...(\because \cos (90^o - \theta) = \sin \theta$ and $\sin (90^o - \theta) = \cos \theta)$
$\Rightarrow \frac{\sin ^{2} 22^{\circ}+\cos ^{2} 22^{\circ}}{\cos ^{2} 22^{\circ}+\sin ^{2} 22^{\circ}} + \sin^2 63^o + \cos^2 63^o$
$\Rightarrow \frac{1}{1} + 1 = 2$
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