8 sin ^{2} 45-2 tan ^{2} 60+3 cot ^{2} 30-2 cos ^{2} 45

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8. Introduction to Trigonometry

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$8 \sin ^{2} 45-2 \tan ^{2} 60+3 \cot ^{2} 30-2 \cos ^{2} 45$

A

$5.5$

B

$6$

C

$4$

D

$5$

Solution

$8 \sin ^{2} 45-2 \tan ^{2} 60+3 \cot ^{2} 30-2 \cos ^{2} 45$

$=8\left(\frac{1}{\sqrt{2}}\right)^{2}-2(\sqrt{3})^{2}+3(\sqrt{3})^{2}-2\left(\frac{1}{\sqrt{2}}\right)^{2}$

$=8\left(\frac{1}{2}\right)-2(3)+3(3)-2\left(\frac{1}{2}\right)$

$=4-6+9-1=6$

Standard 10

Mathematics

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