0 < θ < 90 and sec θ=operatorname{cosec} 60, then value of 2 cos ^{2} θ-1 is ........

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8. Introduction to Trigonometry

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$0 < \theta < 90$ and $\sec \theta=\operatorname{cosec} 60,$ then the value of $2 \cos ^{2} \theta-1$ is ........

A

$3$

B

$1$

C

$\frac{3}{4}$

D

$\frac{1}{2}$

Solution

$\sec \theta=\operatorname{cosec} 60$

$ \therefore \sec \theta=\sec (90-60)$

$ \therefore \sec \theta=\sec 30 $

$ \therefore \theta=30$

Now, $2 \cos ^{2} \theta-1=2 \cos ^{2} 30-1=2\left(\frac{\sqrt{3}}{2}\right)^{2}-1=2\left(\frac{3}{4}\right)-1=\frac{3}{2}-1=\frac{1}{2}$

Standard 10

Mathematics

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