Trigonometric Ratios &amp; Identities · Mathematics · AP EAPCET

$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to

If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to

AP EAPCET 2024 - 22th May Morning Shift

If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

$$ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}= $$

AP EAPCET 2024 - 22th May Morning Shift

If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =

AP EAPCET 2024 - 22th May Morning Shift

If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$

AP EAPCET 2024 - 21th May Evening Shift

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$

Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$

$$ =\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} $$

Which of the following is correct ?

AP EAPCET 2024 - 21th May Evening Shift

If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$

AP EAPCET 2024 - 21th May Evening Shift

If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$

If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$

If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$

If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$

If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is

AP EAPCET 2024 - 20th May Evening Shift

If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

AP EAPCET 2024 - 20th May Evening Shift

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

AP EAPCET 2024 - 20th May Evening Shift

If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$

AP EAPCET 2024 - 20th May Morning Shift

$$ \text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}= $$

AP EAPCET 2024 - 20th May Morning Shift

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=$

AP EAPCET 2024 - 20th May Morning Shift

The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between

AP EAPCET 2024 - 19th May Evening Shift

Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$

Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$

Which one of the following is correct?

AP EAPCET 2024 - 19th May Evening Shift

$ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $

The maximum value of $12\sin x - 5\cos x + 3$ is

$\sin^2 16^\circ - \sin^2 76^\circ = $

By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is

If $$\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta$$, then the least $$n$$ for which $$a_{2 n}=0$$ is

If $$\sin \theta=-\frac{3}{4}$$, then $$\sin 2 \theta=$$

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$$

Which of the following trigonometric values are negative?

I. $$\sin \left(-292^{\circ}\right)$$

II. $$\tan \left(-190^{\circ}\right)$$

III. $$\cos \left(-207^{\circ}\right)$$

IV. $$\cot \left(-222^{\circ}\right)$$

$$\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=$$

A true statement among the following identities is

If $$A+B+C=\pi, \cos B=\cos A \cos C$$, then $$\tan A \tan C=$$

The value of $$\tan \left(\frac{7 \pi}{8}\right)$$ is

$$1+\sec ^2 x \sin ^2 x=$$

If the identity $$\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c$$ holds for some $$a, b, c \in Q$$ then $$(a, b, c)=$$

The value of $$\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$$ is

If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$

$$\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=$$

If $$\operatorname{cosech} x=\frac{4}{5}$$, then $$\sinh x=$$

What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ?

If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third quadrant, then the value of $$\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}$$ is equal to

If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}$$ is equal to

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum value of the AM of $$\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$$ and $$\cos \left(\gamma+\frac{\pi}{2}\right)$$ is equal to

In a $$\triangle A B C$$, if $$3 \sin A+4 \cos B=6$$ and $$4 \sin B+3 \cos A=1$$, then $$\sin (A+B)$$ is equal to

$$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$$ is equal to

If $$f(x)=\frac{\cot x}{1+\cot x}$$ and $$\alpha+\beta=\frac{5 \pi}{4}$$, then the value of $$f(\alpha) f(\beta)$$ is equal to

In $$\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$$, then $$\tan \frac{C}{8}$$ is equal to

Mean of the values $$\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$$ is

When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new system are known to be $$(4,-3)$$. Then find the coordinates of $$P$$ in the original system.

The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is