trigonometric ratios and identities mcq Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024
ibps rrb so officer sclae 2 3 single exam 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Lcm & Hcf
Ratio & Proportion
Percentage
Time & Work
Mensuration
Advance Math
Trigonometric Ratios & Identities
Average
Profit & Loss
What is $√{{1 + sin θ}/{1 - sin θ}}$ equal to?
Answer: (a)
${√{1 + sin θ}}/{√{1 - sin θ}} = √{{(1 + sin θ) (1 + sin θ)}/{(1 - sin θ) (1 + sin θ)}}$
= $√{{(1 + \text"sin θ")^2}/{1 - sin^2 θ}} = √{{(1 + \text"sin θ")^2}/{cos^2 θ}} = {1 + \text"sin θ"}/{\text"cos θ"}$
= $1/{\text"cos θ"} + {\text"sin θ"}/{\text"cos θ"}$ = sec θ + tan θ
What is $sin^6 θ + cos^6 θ + 3sin^2 θ cos^2 θ$ equal to?
Answer: (a)
$sin^6 θ + cos^6 θ + 3 sin^2 θ cos^2 θ$
= $(sin^2 θ)^3 + (cos^2 θ)^3 + 3 sin^2 θ cos^2 θ (sin^2 θ + cos^2 θ)$
[∵ $(a + b)^3 = a^3 + b^3 + 3ab (a + b)]$
= $(sin^2 θ + cos^2 θ)^3 (∵ sin^2 θ + cos^2 θ = 1)$
= $(1)^3$ = 1
The value of ${sin 1°}/{sin 1^c}$ where $1^c$ represents 1 radian is
Answer: (b)
${sin 1°}/{sin 1^c} = {0.0174}/{sin({180}/{π})} = {0.0174}/{0.8415}$ = 0.0206 < 1
If tan 6 θ = cot 2 θ, where 0 < 6 θ < ${π}/2$ , then what is the value of sec 4θ ?
Answer: (b)
tan 6 θ = cot 2 θ
⇒ cot(90° - 6 θ) = cot 2 θ
⇒ 90° - 6 θ = 2 θ
⇒ 8 θ = 90°
∴ 4 θ = 45°
sec 4 θ = sec 45° = $√2$
Consider the following statements :
1. There exists at least one value of x between 0 and ${π}/2$ which satisfies the equation $sin^4 x – 2sin^2$ x – 1 = 0.
2. sin 1.5 is greater than cos 1.5.
Which of the above statements is/are correct?
Answer: (a)
Statement (1)
$sin^4 x - 2 sin^2 x - 1 = 0$
Let $sin^2x$ = t
⇒ $t^2$ - 2t - 1 = 0
⇒ t = ${2 ± 2 √2}/2 ⇒ t = 1 ± √2$
⇒ $sin^2 x = 1 ± √2 i.e., 1 - √2 or 1 + √2$
$sin^2 x$ cannot be -ve.
and sin x lies between -1 and 1
So, for 0 ≤ x ≤ $π/2$ there is no value that satisfies the equation.
∴ (1) is not true.
Statement (2)
sin (1.5) > cos (1.5)
1.5 radian is 1.5 × ${180°}/{π} > 90 in 2^{nd}$ quadrant.
sin (1.5) is +ve but cos (1.5) falls in second where it is - ve.
So, it is always < sin (1.5).
So, only (2) is correct.
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