trigonometric ratios and identities mcq Model Questions & Answers, Practice Test for ibps clerk prelims 2024

Answer: (a)

cos θ = $1/{√5}$

from ΔABC

AB = $√{(AB)^2 + (BC)^2}$

= $√{(√5)^2 - (1)^2} = √{5 - 1} = √4 = 2$

∴ tan θ = ${AB}/{BC} = 2/1 = 2$

Now, ${2 tan θ}/{1 - tan^2 θ} = {2 × 2}/{1 - (2)^2} = - 4/3$

Answer: (a)

cot 1° cot 23° cot 45° cot 67° cot 89°

= cot 1° × cot 23° × cot 45° × cot (90 - 23)° × cot (90 - 1)°

= cot 1° × cot 23° × cot 45° × tan 23° × tan 1° cot 1° × tan 1° × cot 23° × tan 23° × cot 45°

= 1 × 1 × 1 = 1

Answer: (c)

1 and 3 only

sin $1^c$ = sin 57° (approx)

$cos 1^c$ = cos 57°

$tan 1^c = tan 57°$

∴ 180° = ${22^c}/7$

cos 0° = 1, cos 1° = 0.99

cos 57° = 0.54

Answer: (a)

In 60 min h hand gains = 5 min

In 1 min h hand gains = $5/{60}$ min

In 10 min h hand gains = $5/{60} × 10 = 5/6$ min

There is 15 min gap between hours and minutes

hand but in 10 min h hand gains $5/6$ min more.

So, the actual gap = 15 + $5/6 = {95}/6$ min

In 1 min, there are 6°,

In ${95}/6$ min, there are

${95}/6 × 6° = {95}/6 × 6 × {π}/{180} = {19 π}/{36}$ radian

Answer: (c)

sin x : sin y = $√3 : 1 = {√3}/2 : 1/2$

= sin 60° : sin 30°

∴ x : y = 60 : 30

⇒ x : y = 2 : 1.