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8. Introduction to Trigonometry
medium
Evaluate:
$\frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}}$
A
$0$
B
$-1$
C
$1$
D
$0.5$
Solution
$\frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}}$
$=\frac{\left[\sin \left(90^{\circ}-27^{\circ}\right)\right]^{2}+\sin ^{2} 27^{\circ}}{\left[\cos \left(90^{\circ}-73^{\circ}\right)\right]^{2}+\cos ^{2} 73^{\circ}}$
$=\frac{\left[\cos 27^{\circ}\right]^{2}+\sin ^{2} 27^{\circ}}{\left[\sin 73^{\circ}\right]^{2}+\cos ^{2} 73^{\circ}}$
$=\frac{\cos ^{2} 27^{\circ}+\sin ^{2} 27^{\circ}}{\sin ^{2} 73^{\circ}+\cos ^{2} 73^{\circ}}$
$=\frac{1}{1}\left(\right.$ As $\left.\sin ^{2} A+\cos ^{2} A=1\right)$
$=1$
Standard 10
Mathematics
