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
If 7 $sin^2 x + 3 cos^2$ x = 4, 0 < x < 90°, then what is the value of tan x?
Answer: (d)
$7 sin^2 x + 3 cos^2 x = 4$
$7 sin^2 x + 3 -3 sin^2 x = 4$
4 $sin^2 x = 4/3$
sin x = $1/{√3}$
What is the value of $cot^2 θ - (1/{sin^2 θ})$ = ?
Answer: (a)
$cot^2 - 1/{sin^2 θ} = {cos^2 θ}/{sin^2 θ} - 1/{sin^2 θ} = - {sin^2 θ}/{sin^2 θ}$ = -1
If 4 tan θ = 3, then what is ${4 sin θ - cos θ}/{4 sin θ + 9 cos θ}$ equal to?
Answer: (c)
${\text"4 sin θ - cos θ"}/{\text"4 sin θ + 9 cos θ"}$
On dividing both numerator and denominator by cos θ we get
= ${{\text"4 sin θ"}/{\text"cos θ"} - {\text"cos θ"}/{\text"cos θ"}}/{{\text"4 sin θ"}/{\text"cos θ"} + {\text"9 cos θ"}/{\text"cos θ"}}$
Now, put the value of 4 tan θ
${\text"4 tan θ - 1"}/{\text"4 tan θ + 9"} = {3 - 1}/{3 + 9} = 2/{12} = 1/6$
If sin A + cos A = p and $sin^3 A + cos^3$ A = q, then which one of the following is correct?
Answer: (c)
sin A + cos A = p
$sin^3 A + cos^2 A$ = q
$sin^3 A + cos^3 A = (\text"sin A + cos A") (sin^2 A + cos^2 \text"A - sin A cos A")$
q = $p(\text"1 - sin A cos A")$
1 - sin A cos A = $q/p$
1 - sin A cos A = 1 - $q/p = {p - q}/p$
$(\text"sin A + cos A")^3 = p^3$
$sin^3 A + cos^3 \text"A + 3 sin A cos A (sin A + cos A") = p^3$
q + 3 × ${p - q}/p × p = p^3$
$p^3$ = q + 3p - 3q
$p^3$ + 2q - 3p = 0
Let sin(A + B) = ${√3}/2$ and cos B = ${√3}/2$, where A, B are acute angles. What is tan (2A – B) equal to?
Answer: (c)
sin (A + B) = ${√3}/2 ⇒ sin (A + B) = sin ({π}/3)$
∴ A + B = ${π}/3$.....(1)
and cos B = ${√3}/2 ⇒ cos B = cos ({π}/6)$
∴ B = ${π}/6$....(2)
From (1) and (2), we get A = ${π}/3 - {π}/6 = {π}/6$
Hence, tan (2A - B) = tan$(2 × {π}/6 - {π}/6)$
= tan $({π}/3 - {π}/6) = tan ({π}/6) = 1/{√3}$
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