If $f\left(x\right)=\cos x(\sin x+\sqrt{{\sin }^{2}x+{\sin }^2\alpha })$, then

Important Questions on Trigonometric Ratios and Identities

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 1

The value of $\left({\tan }^2\frac{\pi }{7}+{\tan }^2\frac{2\pi }{7}+{\tan }^2\frac{3\pi }{7}\right)\left({\cot }^2\frac{\pi }{7}+{\cot }^2\frac{2\pi }{7}+{\cot }^2\frac{3\pi }{7}\right)$ is equal to...

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 2

The value of ${\tan }^2\frac{\pi }{16}+{\tan }^2\frac{2\pi }{16}+{\tan }^2\frac{3\pi }{16}+......+{\tan }^2\frac{7\pi }{16}$ is equal to...

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 3

If $\sec A\tan B+\tan A\sec B=91$, then the value of $(\sec A\sec B+\tan A\tan B{)}^2$ is equal to...

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 4

If $\frac{9x}{\cos \theta }+\frac{5y}{\sin \theta }=56$ and $\frac{9x\sin \theta }{{\cos }^2\theta }-\frac{5y\cos \theta }{{\sin }^2\theta }=0$, then the value of ${\left[{\left(9x\right)}^{\frac{2}{3}}+{\left(5y\right)}^{\frac{2}{3}}\right]}^3$ is

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 5

If $\alpha +\beta =\gamma$ and $\tan \gamma =22,a$ is the arithmetic and $b$ is the geometric mean respectively between $\tan \alpha$ and $\tan \beta$, then the value of $\frac{a^3}{{\left(1-b^2\right)}^3}$ is equal to

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 10 - Trigonometric Ratios and Identities>EXERCISE>Q 6

If $x,y$ and $z$ are acute angles and $\cos x=\tan y,\cos y=\tan z$ and $\cos z=\tan x$, then $1234\sin x+1342\sin y+1423\sin z=k\sin 18°$ where $k$ is equal to