Higher Math 2nd Paper CQ-Barishal Board-2019

Determine the value of $\sec ^{2}\left(\cos ^{-1} 3\right)+\operatorname{cosec}^{2}\left(\tan ^{-1} 2\right)$.

From scenario- 1 , solve $f(\sin \theta)=0$.

From scenario-2, prove that, $A=\tan ^{-1} \frac{5}{\sqrt{2}}$.

State Lami's theorem.

For scenario 1 if $R=\frac{2}{3} Q$, then find the ratio of $P$ and $Q$.

From scenario-2 show that the resultant is displaced by a distance $\frac{\mathrm{rX}}{\mathrm{P}+\mathrm{Q}}$.

Determine the square root of $-3-4 i$.

By using scenario-1, If $\{p(\omega)\}^{3}+\left\{p\left(\frac{1}{\omega}\right)\right\}^{3}=0$, then show that, $\mathrm{a}=\frac{1}{2}(\mathrm{~b}+\mathrm{c})$ or $\mathrm{c}=\frac{1}{2}(\mathrm{a}+\mathrm{b})$.

From scenario-2, prove that, $1+\omega+\omega^{2}=0$.

Determine the focus of the parabola $x^{2}=4(1-y)$.

According to the scenario-1, find the equation of directrix, equation of latus rectum and length of the latus rectum when the parabola passes through the point $(3,-2)$.

Find the equation of the Conic with the help of scenario-2.

Find the nature of the roots of the equation $4 x^{2}+2 x-1=0.2$

From sœnario-1, prove that $\sqrt{\frac{\mathrm{u}}{\mathrm{v}}}+\sqrt{\frac{\mathrm{v}}{\mathrm{u}}}+\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}=0$.

From scenario-2, find the middle term when $\mathrm{n}=9$ and $\mathrm{n}=12$.