trigonometric ratios and identities mcq Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (c)

We know that, sin θ is increasing in 0° to 90°.

∵ sin30° = $1/2$

∴ sin 32° > $1/2$

Answer: (b)

Only Statement I is correct as tan θ increases faster than sin θ as θ increases while Statement II is wrong as the value of sin θ + cos θ is not always greater than 1. It may also be equal to 1.

Answer: (d)

θ lies is in first quadrant and tan θ = 3

On squaring both sides,

∴ $tan^2$ θ = 9

Add 1 both sides,

⇒ 1 + $tan^2$ θ = 10

⇒ $sec^2$ θ = 10 ⇒ sec θ = $√{10}$

⇒ cos θ = $1/{√{10}}$

∵ $sin^2 θ = 1 - cos^2 θ = 1 - 1/{10} = 9/{10}$

⇒ sin θ = $3/{√{10}}$

Now, sin θ + cos θ = $3/{√{10}} + 1/{√{10}} = 4/{√{10}}$

(θ lies in first quadrant)

Answer: (b)

tan x = a; tan y = b

(a + b) $(1 - 1/{ab}) + (1/a + 1/b)$ (1 - ab)

= ${(a + b)(ab - 1)}/{ab} + {(a + b)(1 - ab)}/{ab}$

= ${(ab - 1 + 1 - ab)(a + b)}/{ab}$ = 0

Answer: (c)

Take θ = 45°

tan θ + cot θ = tan 45° + cot 45° = 1 + 1 = 2

Now, sin θ + cos θ

= sin 45° + cos 45°

= $1/{√2} + 1/{√2} = 2/√2 = √2$