41)

If \(\frac{\sin ^{2} ∅-3 \sin ∅+2}{\cos ^{2} ∅}=1 \), where 0° < ∅ < 90°, then what is the value of (cos 2∅ - sin 3∅ + cosec 2∅)?

SSC CGL 2022

A)

\(\frac{-3-4 \sqrt{3}}{6}\)

B)

\(\frac{3-4 \sqrt{3}}{6}\)

C)

\(\frac{-3+4 \sqrt{3}}{6}\)

D)

\(\frac{3+4 \sqrt{3}}{6}\)

42)

If cosec A = sec B, where A and B are acute angles, then what is the value of (A + B)?

SSC CGL 2022

A)

135°

B)

0°

C)

90°

D)

45°

43)

The value of tan²θ + cot²θ - sec²θ cosec²θ is:

SSC CGL 2022

A)

0

B)

-2

C)

2

D)

1/2

44)

What will be the value of \(\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}} \)?

SSC CGL 2022

A)

1

B)

√2

C)

\(\frac{1}{\sqrt{2}}\)

D)

\(\frac{1}{\sqrt{3}}\)

45)

The value of (sin 30° cos 60°- cos 30° sin60°) is equal to:

SSC CGL 2022

A)

cos 30°

B)

-sin 30°

C)

-cos 30°

D)

sin 30°

46)

What is sin α - sin β?

SSC CGL 2022

A)

\(2 \cos \frac{α-β}{2} \sin \frac{α+β}{2}\)

B)

\(2 \sin \frac{α+β}{2} \sin \frac{α-β}{2}\)

C)

\(2 \cos \frac{α+β}{2} \sin \frac{α-β}{2}\)

D)

\(2 \cos \frac{α+β}{2} \cos \frac{α-β}{2}\)

47)

The value of \({{2 \tan 60°} \over 1+ \tan^260°}\) is:

SSC CGL 2022

A)

sin 60°

B)

tan 60°

C)

cos 60°

D)

sin 30°

48)

What is the value of tan 240°?

SSC CGL 2022

A)

\(\sqrt3\)

B)

\(-\sqrt3\)

C)

\(\sqrt2\)

D)

3

49)

If tan θ + sec θ= 7, being acute, then the value of 5 sin is:

SSC CGL 2022

A)

\({{1} \over 24}\)

B)

\({{24} \over 25}\)

C)

\({{25} \over 24}\)

D)

\({{24} \over 5}\)

50)

\(16 \cos^3 {{\pi } \over 6} - 12 \cos {{\pi } \over 6} =\) _______________.

SSC CGL 2022

A)

1

B)

2

C)

0

D)

-1