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
If $sin^2 60° + cos^2$ (3x – 9°) = 1, then what is the value of x?
Answer: (a)
Given equation can be rewritten as
$cos^2 (3x - 9°) = 1 - sin^2$ 60°
⇒ $cos^2 (3x - 9°) = cos^2 60°$
⇒ 3x - 9° = 60°
⇒ 3x = 69° ⇒ x = 23°
If sin(A + B) = 1, where 0 < B < 45°, then what is cos(A – B) equal to?
Answer: (b)
Given, sin (A + B) = 1
⇒ A + B = $sin^{-1} 1 ⇒ (A + B)$ = 90°
∴ B = 90° - A ⇒ A = 90° - B
cos (A - B) = cos A cos B + sin A sin B
= cos (90 - B) cos B + sin (90 - B) sin B
= sin B cos B + cos B sin B
= 2 sin B cos B = sin 2B
If sin θ cos θ = ${√3}/4$, then $sin^4 θ + cos^4 θ$ is equal to
Answer: (a)
sin θ . cos θ = ${√3}/4$ ......(i)
∴ $sin^4 θ + cos^4 θ = (sin^2 θ + cos^2 θ)^2 - 2 sin^2 θ . cos^2 θ$
= $(1)^2 - 2 (sin θ . cos θ)^2$
= 1 - 2$({√3}/4)^2 = 1 - 2. 3/{16} = 1 - 3/8 = 5/8$
If cos x + $cos^2$ x = 1, then what is the value of $sin^2 x + sin^4$ x = 1= ?
Answer: (a)
Given, cos x + $cos^2 x$ = 1
⇒ cos = $sin^2 x$
On squaring both sides, we get
$cos^2 x = sin^4 x$
⇒ $sin^2 x + sin^4 x$ = 1
What is ${\text"cot A + cosec A" - 1}/{\text"cot A - cosec A" + 1}$ equal to ?
Answer: (b)
${\text"cot A + cosec A - 1"}/{\text"cot A - cosec A + 1"}$
⇒ ${\text"cot A + cosec A" - (cosec^2 \text"A - cot"^2 A)}/{\text"cot A - cosec A + 1"}$
⇒ ${\text"cot A + cosec A [1 - cosec A + cot A"]}/{\text"cot A - cosec A + 1"}$
⇒ cot A + cosec A
⇒ ${\text"cos A"} + {\text"sin A"} = 1/{\text"sin A"} ⇒ {\text"1 + cos A"}/{\text"sin A"}$
ssc cgl tier 1 2024 IMPORTANT QUESTION AND ANSWERS
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SSC CGL Tier 1: Number System Questions PDF For 2024 Exam »
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