(A) We know that $\sec^{2} \theta = 1 + \tan^{2} \theta$. Substituting the value of $\tan \theta = 2$,we get $\sec^{2} \theta = 1 + (2)^{2} = 1 + 4 =

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(A) We know that $\sec^{2} \theta = 1 + \tan^{2} \theta$. Substituting the value of $\tan \theta = 2$,we get $\sec^{2} \theta = 1 + (2)^{2} = 1 + 4 = 5$. Since $\theta$ lies in the third quadrant,$\sec \theta$ must be negative. Therefore,$\sec \theta = -\sqrt{5}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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If $\tan \theta = 2$ and $\theta$ lies in the third quadrant,then the value of $\sec \theta$ is

MHT CET 2020 All MHT CET

A
$-\sqrt{5}$
B
$\sqrt{3}$
C
$-\sqrt{2}$
D
$\sqrt{5}$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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If $\tan \theta = 2$ and $\theta$ lies in the third quadrant,then the value of $\sec \theta$ is

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Prove that $2 \sin ^{2} \frac{3 \pi}{4} + 2 \cos ^{2} \frac{\pi}{4} + 2 \sec ^{2} \frac{\pi}{3} = 10$.

The expression $\frac{\tan(x - \frac{\pi}{2}) \cdot \cos(\frac{3\pi}{2} + x) - \sin^3(\frac{7\pi}{2} - x)}{\cos(x - \frac{\pi}{2}) \cdot \tan(\frac{3\pi}{2} + x)}$ simplifies to:

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Find the degree measure corresponding to the following radian measure (Use $\pi = \frac{22}{7}$):
$-4$ radians