Competitive Exams : Quantitative Aptitude - Trig (Set 9) | Concept of Maths

Question 1

Which of the following is equivalent to the expression $ an 3A - an 2A - an A$?

Accepted Answer

C) $	an 3A 	an 2A 	an A$

Answer

A) $	an 3A 	an 2A + 	an A$

Answer

B) $\cot 3A \cot 2A \cot A$

Answer

D) $	an 6A$

Question 2

Find the minimum value of the expression $9 an^2 heta + 4 \cot^2 heta$ for $0 < heta < \frac{\pi}{2}$.

Accepted Answer

B) 12

Answer

A) 6

Answer

C) 13

Answer

D) 18

Question 3

Simplify the expression: $4 \sin heta \sin(60^\circ - heta) \sin(60^\circ + heta)$.

Accepted Answer

A) $\sin 3	heta$

Answer

B) $\cos 3	heta$

Answer

C) $3 \sin 	heta$

Answer

D) $4 \sin 3	heta$

Question 4

If $\cos \alpha + \cos \beta = 0$ and $\sin \alpha + \sin \beta = 0$, what is the value of $\cos 2\alpha + \cos 2\beta$?

Accepted Answer

D) $-2 \cos(\alpha + \beta)$

Answer

A) 0

Answer

B) 1

Answer

C) -1

Question 5

Solve for the value of $\sin(\cot^{-1}(\cos( an^{-1} x)))$.

Accepted Answer

B) $\sqrt{\frac{x^2+1}{x^2+2}}$

Answer

A) $\sqrt{\frac{x^2+1}{x^2+3}}$

Answer

C) $\frac{x}{\sqrt{x^2+2}}$

Answer

D) 1

Question 6

Find the value of $\cos 12^\circ + \cos 84^\circ + \cos 156^\circ + \cos 132^\circ$.

Accepted Answer

C) $-1/2$

Answer

A) 0

Answer

B) $1/2$

Answer

D) -1

Question 7

If $\sec heta + an heta = p$, then what is the value of $\sin heta$?

Accepted Answer

A) $\frac{p^2-1}{p^2+1}$

Answer

B) $\frac{p^2+1}{p^2-1}$

Answer

C) $\frac{2p}{p^2+1}$

Answer

D) $\frac{p^2-1}{2p}$

Question 8

A ladder 15m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, find the height of the wall.

Accepted Answer

D) 7.5 m

Answer

A) 15 m

Answer

B) $15\sqrt{3}$ m

Answer

C) $\frac{15\sqrt{3}}{2}$ m

Question 9

Find the number of solutions for the equation $\sin^2 heta - \cos heta = \frac{1}{4}$ in the interval $[0, 2\pi]$.

Accepted Answer

C) 2

Answer

A) 1

Answer

B) 0

Answer

D) 4

Question 10

If $A + B + C = 180^\circ$, what is the value of $ an A + an B + an C$?

Accepted Answer

B) $	an A 	an B 	an C$

Answer

A) 0

Answer

C) 1

Answer

D) -1