Trigonometry (10)
Trigonometric Ratios, Trigonometric Identities, Heights and Distances.
From the top of a 7 m high building, the angle of elevation of the top
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°.
...The shadow of a tower standing on a level ground is found to be 40 m
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 was 60°. Find the height
...Prove that $ \frac{1 + tan^2 A}{1 + cot^2 A} = sec^2A -1 $
Prove that $ \frac{1 + tan^2 A}{1 + cot^2 A} = sec^2A -1 $
If $ \sin\alpha = \frac{1}{2} $, then find the value of $ 3 \cos \alpha − 4 cos^3 \alpha $
If $ \sin\alpha = \frac{1}{2} $, then find the value of $ 3 \cos \alpha − 4 cos^3 \alpha $
The angle of elevation of the top of a 30 m high tower
The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is
...The value of $ 5 \sin^2 90^{\circ} - 2 cos^20^{\circ} $ is
The value of $ 5 \sin^2 90^{\circ} - 2 cos^20^{\circ} $ is
...If $ \triangle ABC \sim \triangle DEF $ and $ \angle A = 47^{\circ}, \angle E = 83^{\circ} $
If $ \triangle ABC \sim \triangle DEF $ and $ \angle A = 47^{\circ}, \angle E = 83^{\circ} $, then $ \angle C $ is equal
...As observed from the top of a 100 m high light house
As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is
...Prove that: $ \frac{\sin A - 2 \sin^3 A} {2 \cos^3 A – \cos A} = \tan A $
Prove that: $ \frac{\sin A - 2 \sin^3 A} {2 \cos^3 A – \cos A} = \tan A$
If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A
If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.
$ If 4 \tan \theta = 3, evaluate \frac{4 \sin\theta - \cos\theta + 1}{4 \sin\theta + \cos \theta - 1}$
$ If 4 \tan \theta = 3, evaluate \frac{4 \sin\theta - \cos\theta + 1}{4 \sin\theta + \cos \theta - 1}$
What is the value of $(cos^2 67° - sin^2 23°)$
What is the value of $(cos^2 67° – sin^2 23°)$ ?
An aeroplane is flying at a height of 300 m above the ground
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on
...On a straight line passing through the foot of a tower, two points C and D
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the
...If a tower 30 m high, casts a shadow $10\sqrt{3}$ m long on the ground
If a tower 30 m high, casts a shadow $10\sqrt{3}$ m long on the ground, then what is the angle of elevation of the sun ?
Prove that: $\frac{\sin\theta} {\cot\theta +\csc\theta}$ = 2 + $\frac{\sin\theta}{\cot\theta - \csc\theta}$
Prove that:
$\frac{\sin\theta} {\cot\theta +\csc\theta}$ = 2 + $\frac{\sin\theta}{\cot\theta - \csc\theta}$
Prove that: $\frac{\tan\theta} {1- \cot\theta}$ + $\frac{\cot\theta}{1-\tan\theta}$ = $1 + \sec\theta \csc\theta$
Prove that:
$\frac{\tan\theta} {1- \cot\theta}$ + $\frac{\cot\theta}{1-\tan\theta}$ = $1 + \sec\theta \csc\theta$
Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him
Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of
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$\sin^2 60^{\circ} + 2 \tan 45^{\circ} – \cos^2 30^{\circ} $
Evaluate: $\sin^2 60^{\circ} + 2 \tan 45^{\circ} – \cos^2 30^{\circ} $