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8. Introduction to Trigonometry
medium
For acute angle $\theta,$ if $\cos \theta=\sin \theta,$ then $2 \tan ^{2} \theta+\sin ^{2} \theta+1=\ldots \ldots \ldots \ldots$
A
$\frac{5}{2}$
B
$\frac{7}{4}$
C
$\frac{5}{4}$
D
$\frac{7}{2}$
Solution
$\cos \theta=\sin \theta \quad \therefore \frac{\cos \theta}{\cos \theta}=\frac{\sin \theta}{\cos \theta} \quad \therefore 1=\tan \theta \quad \therefore \theta=45$
$2 \tan ^{2} \theta+\sin ^{2} \theta+1=2 \tan ^{2} 45+\sin ^{2} 45+1$
$=2(1)^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2}+1$
$=2+\frac{1}{2}+1=3+\frac{1}{2}=\frac{7}{2}$
Standard 10
Mathematics
