Trigonometric Ratios of Some Specific Angles

If $\tan \theta -\cot \theta =0,$ then the value of $\sin \theta +\cos \theta ?$

If $cot\theta ·cot30°=1$, then what is the value of $cot\left(\theta +30°\right)$?

$\sin 30°\cos 60°+\cos 30°\sin 60°=\tan 90°$.

A contractor wants to set up a slide for the children to play in the park. He wants to set it up at the height of $2 \mathrm{m}$ and by making an angle of $30°$ with the ground. What should be the length of the slide?

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making $30°$ angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is $6 \mathrm{m}$. Find the height of the tree before falling down.

From figure, find the values of  $\sin A \cos C + \cos A \sin C$ 

From figure, find the values of  ${\sin }^{2}A+{\sin }^{2}C$ 

If the angle $\theta =-30°$, find the value of $\sin \theta$ and $\cos \theta$

A kite is attached to a $100 \mathrm{m}$ long string. Find the greatest height reached by the kite, when its string makes an angle of $60°$ with the level ground.

From the top of a tower of $50 \mathrm{m}$ high, Neha observes the angles of depression of the top and foot of another building to be $45°$ and $60°$ respectively. Find the height of the building to the nearest whole number (in $\mathrm{m}$). Assume $\sqrt{3}=1.732$.

If $\theta =45°$, then find $\tan \theta$.

Find the length of the altitude (in $\mathrm{cm}$) of an equilateral triangle with side $6 \mathrm{cm}$. $\left(\sqrt{3}=1.73\right)$

A pole and its shadow have same length, find the angle of the sun ray made with the earth at that time.

In right-angled triangle $PQR$, if hypotenuse $PR=12$ and $PQ=6$, then what is the measure of $\angle P$?

Find the value of $\frac{{\tan }^2 60°+{\cot }^2 30°}{{\sin }^2 30°+{\cos }^2 60°}$.

If $\sin \theta =\frac{1}{2}$, then the value of $\theta =k°$. Find the value of $k$.

Find the value of $\tan 45°+\cot 45°.$

Find the value: $3\cos 30°-4{\cos }^{3}30°$

Find the value of ${\tan }^{2}60°+3{\cos }^{2}30°$ in mixed fraction form.

Find the value of $\frac{4}{{\cot }^{2}30°}+\frac{1}{{\sin }^{2}30°}-{\cos }^{2}45°$.