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8. Introduction to Trigonometry
medium
$2 \sin ^{2} \theta+4 \sec ^{2} \theta+5 \cot ^{2} \theta+2 \cos ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta=\ldots \ldots \ldots$
A
$4$
B
$3$
C
$2$
D
$1$
Solution
$2 \sin ^{2} \theta+4 \sec ^{2} \theta+5 \cot ^{2} \theta+2 \cos ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta$
$=2 \sin ^{2} \theta+2 \cos ^{2} \theta+4 \sec ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta+5 \cot ^{2} \theta$
$=2\left(\sin ^{2} \theta+\cos ^{2} \theta\right)+4\left(\sec ^{2} \theta-\tan ^{2} \theta\right)-5\left(\operatorname{cosec}^{2} \theta-\cot ^{2} \theta\right)$
$=2(1)+4(1)-5(1)$
$=2+4-5=1$
Standard 10
Mathematics
