Trigonometry (10)

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 longer when the Sun’s altitude is 30° than when it was 60°. Find the height

Prove that $\frac{1+ta{n}^{2}A}{1+co{t}^{2}A}=se{c}^{2}A-1$

If $\sin \alpha =\frac{1}{2}$, then find the value of $3\cos \alpha -4co{s}^3\alpha$

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 $5{\sin }^2{90}^{\circ }-2co{s}^2{0}^{\circ }$ is

If $\mathrm{△}ABC\sim \mathrm{△}DEF$ and $\mathrm{\angle }A={47}^{\circ },\mathrm{\angle }E={83}^{\circ }$, then $\mathrm{\angle }C$ is equal

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: $\frac{\sin A-2{\sin }^{3}A}{2{\cos }^{3}A–\cos A}=\tan A$

If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.

$If4\tan \theta =3,evaluate\frac{4\sin \theta -\cos \theta +1}{4\sin \theta +\cos \theta -1}$

What is the value of $(co{s}^{2}67°–si{n}^{2}23°)$ ?

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 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,  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:

$\frac{\tan \theta }{1-\cot \theta }$ + $\frac{\cot \theta }{1-\tan \theta }$ = $1+\sec \theta \csc \theta$

Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of

If sin A = $\frac{3}{4}$ , calculate sec A.

Evaluate: ${\sin }^2{60}^{\circ }+2\tan {45}^{\circ }–{\cos }^2{30}^{\circ }$