Exams › SSC CGL (Prelims) › General

If \(\cos A - \sin A = \sqrt{3}\cos A\), what is \(\tan A\)?

1. √3
2. 1
3. √3 - 1
4. 1 - √3

Correct answer: 1 - √3

Solution

Rearranging gives \(-\sin A = (\sqrt{3}-1)\cos A\). Dividing by \(\cos A\), we get \(-\tan A = \sqrt{3}-1\), so \(\tan A = 1-\sqrt{3}\).

Related SSC CGL (Prelims) General questions

• If \(\cos(90^\circ-\theta)=\sin(2\theta)\), what is \(\theta\)?
• Given that angles \(A\) and \(B\) are complementary and \(\cos A=\frac{5}{13}\), what is \(\tan B\)?
• What is the radian measure of $135^\circ$?
• If $\sin^2\theta-\cos^2\theta=-\frac{1}{3}$, find the value of $\cos^2\theta$.
• If \(\tan B = \cot(4B - 45^\circ)\), what is \(B\)?
• A vertical tower of height \(H\) stands on the ground. From point A on the ground, the angle of elevation to the top is \(45^\circ\). From point B, located 15 meters away from A along the line extending from the base, the angle of elevation is \(30^\circ\). What is the height of the tower?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →