Evaluate the value of the expression: sin ⁡ 25 ∘ sin ⁡ 65 ∘ − cos ⁡ 25 ∘ cos ⁡ 65 ∘ \sin 25^\circ \sin 65^\circ - \cos 25^\circ \cos 65^\circ sin 2 5 ...

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...

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

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

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

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