Trigonometric Ratios

Let $PQR$ be a right-angled triangle, right-angled at $R$. Given $PQ = 29 \text{ cm}$, $QR = 21 \text{ cm}$, and $\angle...

Let $\triangle ABC$ be a right-angled triangle with the right angle at $B$. If $\tan A = \sqrt{3}$, then find the values...

If $\tan(x + y) \times \tan(x - y) = 1$, then find the value of $\tan x$....

If $$\frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta} = \frac{1}{9}$$ and $$\theta$$ lies in the first quadra...

Two ships are on the opposite sides of a lighthouse such that all three of them are collinear. The angles of depression ...

If $\tan(A + B) = \sqrt{3}$ and $\tan(A - B) = \frac{1}{\sqrt{3}}$ with $0^\circ < (A + B) < 90^\circ$ and $A > B$, then...

Evaluate the value of the expression: $$\sin 25^\circ \sin 65^\circ - \cos 25^\circ \cos 65^\circ$$...

The angle of elevation of the top of a building at a distance of $70 \text{ m}$ from its foot on a horizontal plane is f...

Select the INCORRECT formula from the following options: 1. $\csc^{2} \theta - \cot^{2} \theta = 1$ 2. $\sin^{2} \theta...

From the top of an upright pole $24\sqrt{3}$ feet high, the angle of elevation of the top of an upright tower was $60^\c...

Find the exact value of $\cos 120^\circ$:...

In a right-angled triangle $\triangle ABC$ right angled at $B$, given $AB = 12 \text{ cm}$ and $\angle CAB = 60^\circ$, ...

Evaluate the expression: $$(\sin \theta + \csc \theta)^2 + (\cos \theta + \sec \theta)^2 = ?$$...

If \( a \cot \theta + b \csc \theta = p \) and \( b \cot \theta + a \csc \theta = q \), then find the value of \( p^2 - ...

The angle of elevation of the top of a tower from the top of a building whose height is $680 \text{ m}$ is $45^\circ$ an...

Two pillars of equal height stand on either side of a roadway which is $150 \text{ m}$ wide. At a point in the road betw...

From the top of a tower, the angle of depression of the top of a 10 m high building is $60^\circ$. If the distance betwe...

If $\sin A = \frac{5}{13}$, then find the value of $$\frac{\cos A - 2 \tan A}{\sin A + 3 \tan A}$$...

In triangle PQR, right-angled at R, with $PQ = 29 \text{ cm}$, $QR = 21 \text{ cm}$ and $\angle Q = \theta$, find the va...

If $\cos 27^\circ = \frac{p}{q}$, then find the value of $\csc 27^\circ - \cos 63^\circ$....

If $\sin A = \frac{5}{13}$, then find the value of $$\frac{\cos A - 2 \tan A}{\sin A + 3 \tan A}$$...

If $\cos 27^\circ = \frac{p}{q}$, then find the value of $\csc 27^\circ - \cos 63^\circ$....