problem archive
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Choose the correct option and justify your choice: (i) \( \frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} \) (A) \( \sin 60^\circ \) (B) \( \cos 60^\circ ... -
If \( \tan (A + B) = \sqrt{3} \) and \( \tan (A - B) = \frac{1}{\sqrt{3}} \) ; \( 0^\circ < A + B \leq 90^\circ \) ; \( A > B \), find A and B. -
State whether the following are true or false. Justify your answer. (i) \( \sin (A + B) = \sin A + \sin B \). (ii) The value of \( \sin \theta \) incr... -
Express the ratios cos A, tan A and sec A in terms of sin A. -
Prove that sec A (1 - sin A)(sec A + tan A) = 1. -
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. -
Write all the other trigonometric ratios of ∠A in terms of sec A. -
Choose the correct option. Justify your choice. (i) 9 sec² A − 9 tan² A = (A) 1 (B) 9 (C) 8 (D) 0 (ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ) = (A)... -
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) (cosec θ − cot θ)² = 1 − cos θ /... -
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top ... -
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the... -
From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the an... -
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the... -
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Fi... -
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the br... -
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between ... -
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide wh... -
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the... -
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination o... -
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases fro...