FOR INTERNAL ASSESSMENT

In a triangle $ABC$,  $\angle C=90°$ and $\tan A=\frac{1}{\sqrt{3}}$. Find the value of $\sin A.\cos B+\cos A.\sin B$.

In a triangle $ABC$,  $\angle C=90°$ and $\tan A=\frac{1}{\sqrt{3}}$. Find the values of $\cos A.\cos B-\sin A.\sin B$.

From a point $O$ on the ground, the angle of elevation of the top of a tower is $30°$ and that of the top of the flagstaff on the top of the tower is $60°$. If the length of the flagstaff is $5$ metres, find the height of the tower.

A man on the cliff observes a boat at an angle of depression of $30°$ which is approaching the seashore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be $60°$. Find the total time taken(in minutes) by the boat to reach the shore.

Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

In the figure, the sides $AB, BC$ and $CA$ of a triangle $ABC$ touch a circle with centre $O$ and radius $\text{'}r\text{'}$ at $P, Q$ and $R$ respectively.

Prove that $AB+CQ=AC+BQ$.

In the figure, the sides $AB, BC$ and $CA$ of a triangle $ABC$ touch a circle with centre $O$ and radius $\text{'}r\text{'}$ at $P, Q$ and $R$ respectively.

Prove that ar$(△ABC)=\frac{1 }{2}(\mathrm{perimeter} \mathrm{of} △ABC)\times r$.

Draw a more than ogive for the data given below, which gives the marks of $100$ students