Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMix Examples-Trigonometrical Ratios, Functions and Identities
DifficultIf $\alpha \in (0, \pi/2)$,then $\sqrt{x^2 + x} + \frac{\tan^2 \alpha}{\sqrt{x^2 + x}} = \dots$
- A$2 \tan \alpha$
- B$1$
- C$2$
- D$\sec^2 \alpha$
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Similar Questions
Prove that $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$.
Medium
View SolutionIf $\sin \theta + \cos \theta = \frac{1}{2}$,then $16(\sin(2\theta) + \cos(4\theta) + \sin(6\theta))$ is equal to:
For a positive integer $n$,let ${f_n}(\theta ) = \left( {\tan \frac{\theta }{2}} \right)(1 + \sec \theta )(1 + \sec 2\theta )(1 + \sec 4\theta ) \dots (1 + \sec {2^n}\theta ).$ Then
DifficultIIT 1999
View SolutionThe number of $x \in [0, 2\pi]$ for which $|\sqrt{2 \sin^4 x + 18 \cos^2 x} - \sqrt{2 \cos^4 x + 18 \sin^2 x}| = 1$ is
DifficultJEE MAIN 2016
View SolutionIf $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2a$,then the value of $\left(a+\frac{1}{a}\right)$ is:
DifficultJEE MAIN 2023
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