Prove that : $\cos ^2 A+\frac{1}{1+\cot ^2 A}=1$.
View full solution →Question types
Trigonometry question types
156 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
156
Questions
5
Question groups
5
Question types
01
[1 Mark Question Answer]
9 Q→02[2 Mark Question Answer]
46 Q→03[3 marks sum]
53 Q→04[5 marks sum]
12 Q→05[4 marks sum]
36 Q→Sample Questions
Trigonometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Prove the following identity :$\left(1-\sin ^2 \theta\right) \sec ^2 \theta=1$
View full solution →From the trigonometric table, write the values of tan 45°48'.
From the trigonometric table, write the values of cos 23°17'.
From trigonometric table, write the values of sin 37°19'.
Prove that $\sqrt{2+\tan ^2 \theta+\cot ^2 \theta}=\tan \theta+\cot \theta$.
View full solution →Prove that:
$\frac{\cos ^3 \theta+\sin ^3 \theta}{\cos \theta+\sin \theta}+\frac{\cos ^3 \theta-\sin ^3 \theta}{\cos \theta-\sin \theta}=2$
View full solution →$\frac{\cos ^3 \theta+\sin ^3 \theta}{\cos \theta+\sin \theta}+\frac{\cos ^3 \theta-\sin ^3 \theta}{\cos \theta-\sin \theta}=2$
Prove the following identity : $\frac{\left(1+\tan ^2 A\right) \cot A}{\cos e c^2 A}=\tan A$
View full solution →Prove that : $\left(1+\frac{\cot ^2 \theta}{1+\operatorname{cosec} \theta}\right)=\operatorname{cosec} \theta$.
View full solution →Prove that identity:
$\frac{\sec A-1}{\sec A+1}=\frac{1-\cos A}{1+\cos A}$
View full solution →$\frac{\sec A-1}{\sec A+1}=\frac{1-\cos A}{1+\cos A}$
A pole being broken by the wind the top struck the ground at an angle of $30^\circ$ and at a distance of $8\ m$ from the foot of the pole. Find the whole height of the pole.
View full solution →A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7 meters. At a point in a plane, the angle of elevation of the bottom and the top of the flagstaff are respectively 30° and 60°. Find the height of the tower.
An aeroplane when $3,000$ meters high passes vertically above another aeroplane at an instance when their angles of elevation at the same observation point are $60°$ and $45°$ respectively. How many meters higher is the one than the other?
View full solution →From a window $A , 10\ m$ above the ground the angle of elevation of the top $C$ of a tower is $X^\circ$, Where tan $x^{\circ}=\frac{5}{2}$ and the angle of depression of the foot $D$ of the tower is $Y^\circ,$ Where tan $y^{\circ}=\frac{1}{4}$. calculate the height $CD$ of the tower in metres .
View full solution →In triangle ABC, AB = 12 cm, LB = 58°, the perpendicular from A to BC meets it at D. The bisector of angle ABC meets AD at E. Calculate:
(i) The length of BD;
(ii) The length of ED.
Give your answers correct to one decimal place.
(i) The length of BD;
(ii) The length of ED.
Give your answers correct to one decimal place.
A man on the top of vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes $12$ minutes for the angle of depression to change from $30^\circ$ to $45^\circ$, how soon after this will the car reach the observation tower? (Give your answer correct to nearest seconds).
View full solution →The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. Find the height of the tower, correct to two decimal places.
A man observes the angle of elevation of the top of a building to be 30°. He walks towards it in a horizontal line through its base. On covering 60 m, the angle of elevation changes to 60°. Find the height of the building correct to the nearest metre.
A man on the deck of a ship is 10 m above water level. He observes that the angle of elevation of the top of a cliff is 42° and the angle of depression of the base is 20°. Calculate the distance of the cliff from the ship and the height of the cliff.
If the angle of elevation of a cloud from a point h meters above a lake is a*and the angle of depression of its reflection in the lake is |i. Prove that the height of the cloud is $\frac{h(\tan \beta+\tan \alpha)}{\tan \beta-\tan \alpha}$.
View full solution →Two men on either side of a temple 75 m high observed the angle of elevation of the top of the temple to be 30° and 60° respectively. Find the distance between the two men.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate:
(i) the width of the river;
(ii) the height of the tree.
From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be 30° and 45° respectively. Find the distances of the two stones from the foot of the hill.
From a lighthouse, the angles of depression of two ships on opposite sides of the lighthouse were observed to be $30^\circ$ and $45^\circ.$ If the height of the lighthouse is $90$ metres and the line joining the two ships passes through the foot of the lighthouse, find the distance between the two ships, correct to two decimal places.
View full solution →The angle of elevation of a cloud from a point 200 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.
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