List of top Questions asked in AP EAPCET- 2022

\( \cos\theta (\csc\theta - \sec\theta) - \cot\theta = \)
If the identity $\cos^4\theta = a\cos4\theta + b\cos2\theta + c$ holds for some $a, b, c \in \mathbb{Q}$, then $(a, b, c) =$ ?
If $ \sin\theta + \csc\theta = 4 $, then find: $$ \sin^2\theta + \csc^2\theta = ? $$
\( \frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x} = \)
Evaluate: $$ \sin^2\left(\frac{2\pi}{3}\right) + \cos^2\left(\frac{5\pi}{6}\right) - \tan^2\left(\frac{3\pi}{4}\right) $$
A true statement among the following identities is
$1 + \sec^2 x \cdot \sin^2 x = $
The value of \( \sin(\frac{5\pi}{24}) \cdot \cos(\frac{\pi}{24}) \) is
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
The smallest integer \( n \) such that \[ \frac{1}{\sin 45^\circ \sin 46^\circ} + \frac{1}{\sin 47^\circ \sin 48^\circ} + \cdots + \frac{1}{\sin 133^\circ \sin 134^\circ} = \frac{1}{\sin(n^\circ)} \]
In any triangle ABC, \( \frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2} = \)
In triangle $ ABC $, if: $$ r_1 = 36,\quad r_2 = 18,\quad r_3 = 12 $$ then find the semi-perimeter $ s $.
If $ \sin \theta = -\frac{3}{4} $, then compute $ \sin 2\theta $
In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]
In any triangle $ ABC $, evaluate: $$ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} $$
If $$ \sin^4 \theta \cos^2 \theta = \sum_{n=0}^{\infty} a_{2n} \cos 2n\theta $$ then the least value of $ n $ for which $ a_{2n} = 0 $ is:
\( 2\cot^2\theta - \cot\theta - 3 = \) (The question implies factorization of the quadratic in \(\cot\theta\))
Evaluate: $$ \frac{1}{\sin 1^\circ \sin 2^\circ} + \frac{1}{\sin 2^\circ \sin 3^\circ} + \cdots + \frac{1}{\sin 89^\circ \sin 90^\circ} $$
Let \( z = x + iy \) be a complex number with \( x, y \in \mathbb{Z} \). Then the area (in square units) of the rectangle whose vertices are the roots of the equation \( \bar{z} \cdot z^3 + z \cdot \bar{z}^3 = 350 \) is:
Let \( f(x) = x^2 + \frac{1}{x^2} \) and \( g(x) = x - \frac{1}{x} \) for \( x \in \mathbb{R} \setminus \{-1, 0, 1\} \). Then, the local minimum of \( \frac{f(x)}{g(x)} \) is:
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
Let \(f: R \rightarrow R\) be defined by \(f(x) = 2x+3\). If \(\alpha, \beta\) are the roots of the equation \(f(x^2) - 2f(\frac{x}{2}) - 1 = 0\) then \(\alpha^2 + \beta^2 = \)
If a function \( f: \mathbb{R} - \{l\} \to \mathbb{R} - \{m\} \) defined by \( f(x) = \frac{x+3}{x-2} \) is a bijection, then \( 3l + 2m = \) ?
Let $ f : \mathbb{R} - \left\{-\frac{1}{2}\right\} \rightarrow \mathbb{R} $ be defined by $$ f(x) = \frac{x - 2}{2x + 1} $$ If $ \alpha, \beta $ satisfy the equation $$ f(f(x)) = -x $$ then evaluate: $$ 4(\alpha^2 + \beta^2) $$
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)