trigonometric ratios and identities Model Questions & Answers, Practice Test for ssc cgl tier 1 2024
ssc cgl tier 1 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Ratio & Proportion
Percentage
Time & Work
Time & Distance
Trigonometric Ratios & Identities
What is the angle subtended at the centre of a circle of radius 8 m after traversing 4 π m along its circumference?
Answer: (a)
Angle subtended = ${Arc}/{Radius} = {4 π}/8 = {π}/2$
Consider the following statements :
1. sin66° is less than cos66°
2. sin26° is less than cos26°
Which of the above statements is/are correct ?
Answer: (a)
From the graph it is clear that
sin θ > cos θ when ${π}/4 θ ≤ {π}/2$
and sin θ < cos θ, when 0 ≤ 0 ≤ ${π}/4$
So, option (b) is correct.
What is the value of $[(1 – sin^2 θ) sec^2 θ + tan^2 θ] (cos^2 θ + 1)$ when 0° < θ < 90°?
Answer: (a)
$[(1 - sin^2 θ) sec^2 θ + tan^2 θ] (cos^2 θ + 1)$
$(∵ sin^2 θ + cos^2 θ = 1)$
= $[cos^2 θ . sec^2 θ + tan^2 θ] (cos^2 θ + 1)$
= $(1 + tan^2 θ) (cos^2 θ + 1) (∵ sec^2 θ - tan^2 θ = 1)$
= $sec^2 θ (cos^2 θ + 1)$
= $sec^2 θ. cos^2 θ + sec^2 θ$
= 1 + $sec^2$ θ > 1 + 1 > 2
(∵ $sec^2$ θ > 1 for θ < θ < 90°)
What is $sin^4 θ – cos^4$ θ equal to for any real number θ?
Answer: (d)
$sin^4 θ - cos^4 θ$
= $(sin^2 θ)^2 - (cos^2 θ)^2 = (sin^2 θ + cos^2 θ) (sin^2 θ - cos^2 θ)$
1$(sin^2 θ - cos^2 θ) = 1 - cos^2 θ - cos^2 θ = 1 - 2 cos^2 θ$
${cos θ}/{1 - sin θ} - {cos θ}/{1 + sin θ}$ = 2 is satisfied by which one of the following values of θ ?
Answer: (c)
Given, ${\text"cos θ"}/{\text"1 - sin θ"} - {\text"cos θ"}/{\text"1 + sin θ"}$ = 2
⇒ ${\text"cos θ + sin θ cos θ - cos θ + cos θ sin θ"}/{1 - sin^2 θ}$ = 2
⇒ $\text"2 sin θ cos θ = 2" cos^2$ θ
⇒ $cos^2$ θ (tan θ - 1) = 0
⇒ tan θ = 1 and cos θ ≠ 0 ⇒ θ = ${π}/4$
ssc cgl tier 1 2024 IMPORTANT QUESTION AND ANSWERS
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