Higher Math 2nd Paper CQ-Chittagong Board-2021

Solve: $\tan ^{2} \theta-3 \operatorname{cosec}^{2} \theta+1=0$.

If $a=\sqrt{3}$ and $b=1$, solve the equation from scenario-1, when $-2\pi<x<2\pi$

According to scenario-2, solve the equation $f(x)+$ $\mathrm{f}(3 \mathrm{x})+\mathrm{f}(5 \mathrm{x})+\mathrm{f}(7 \mathrm{x})=0$; when $0<\mathrm{x}<\pi$.

If the line $y=2 x+c$ touches the ellipse $8 x^{2}+4 y^{2}$ $=12$, find the value of $c$.

From scenario-1, find the foci and the length of the latus rectum of the conic.

According to scenario-2, find the equation of the hyperbola, where eccentricity is $\sqrt{3}$.

Find the eccentricity of $3 x^{2}+5 y^{2}=1$.

From scenario-1, find vertex, focus, equations of latus rectum and directrix.

According to scenario-2, find the equation of the parabola.

Find the nature of the roots of the equation $3 x^{2}+$ $2 x+5=0$.

According to the scenario-1, find the equation whose roots are $\alpha+\beta$ and $\alpha \beta$.

According to the scenario-2, if the two equations have a common root, find the value of $k$.

Prove that, $\operatorname{cosec}^{2}\left(\tan ^{-1} \frac{1}{2}\right)-3 \sec ^{2}\left(\cot ^{-1} \sqrt{3}\right)=1$.

If $f(\pi g(x))=g(\pi f(x))$; show that, $\theta= \pm \frac{1}{2} \sin ^{-1} \frac{3}{4}$.

According to the stem prove that, $2 \mathrm{~A}+\mathrm{B}=2$ (C +D).