Exercise

The ratio of the volumes of a right circular cylinder and a sphere is $1:3$ and ratio of the radius of the cylinder and the sphere $1:3$. If the sum of the height and radius of the cylinder is $78 \mathrm{cm}$, find the height of the cylinder.

If $4 \mathrm{tan\theta }=3$, evaluate $\left(\frac{4\mathrm{sin\theta }-\mathrm{cos\theta }+1}{4\mathrm{sin\theta }+\mathrm{cos\theta }-1}\right)$.

 If the point $C\left(-1,2\right)$ divides internally the line segment joining $A\left(2,5\right)$ and $B\left(x,y\right)$ in the ratio $3:4$, find the coordinates of $B$.

Find the coordinates of a point $A$, where $AB$ is diameter of a circle whose centre is $\left(2,-3\right)$ and $B$ is the point $\left(1,4\right)$. 

Solve:

$x^2={\sin }^2\left(30°\right)+4co{t}^2\left(45°\right)-se{c}^2\left(60°\right)$

Prove that $\frac{\sin \theta -2{\sin }^3\theta }{2{\cos }^3\theta -\cos \theta }=\tan \theta$.

Find the H.C.F of $1260$ and $7344$ using Euclid's algorithm.

Prove that: $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=cosec\theta +cot\theta$.