Trigonometric Ratios & Identity Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Trigonometric Ratios & Identities PRACTICE TEST [1 - EXERCISES]
Trigonometric Ratios & Identity Model Questions Set 1
Question : 21
Suppose 0 < θ < 90°, then for every θ, 4 $sin^2$ θ + 1 is greater than or equal to
a) 4 sin θ
b) 2
c) 4 cos θ
d) 4 tan θ
Answer »Answer: (a)
Let 4 $sin^2$ θ + 1 ≥ 4 sin θ
4 $sin^2$ θ - 4 sin θ + 1 ≥ 0
$(2 sin θ - 1)^2 ≥ 0$
sin θ ≥ $1/2$
Question : 22
What is the value of x in the equation $x {cosec^2 30 ° sec^2 45 °}/{8 cos^2 45 ° sin^2 60 °} = tan^2 60° – tan^2 30° $ ?
a) x = 2
b) x = 1
c) x = $1/2$
d) x = $3/2$
Answer »Answer: (b)
Given, x ${cosec^2 30° sec^2 45°}/{8 cos^2 45° sin^2 60°} = tan^2 60° - tan^2 30°$
⇒ ${x × (2)^2 × (√2)^2}/{8 × (1/{√2})^2 × ({√3}/2)^2} = (√3)^2 - (1/{√3})^2$
⇒ ${x × 4 × 2 × 4}/{8 × 1/2 × 3} = 3 - 1/3$
⇒ ${8x}/3 = 8/3 ⇒$ x = 1
Question : 23
If x lies in the first quadrant and cos x = $5/{13}$, what is the value of tan x – cot x?
a) ${139}/{60}$
b) ${–139}/{60}$
c) ${119}/{60}$
d) None of these
Answer »Answer: (c)
Given that, cos x = $5/{13} = {Base}/{Hypotenuse}$
P = $√{h^2 - b^2} = √{13^2 - 5^2}$
= $√{169 - 25} = √{144}$ = 12
∴ tan x - cot x = $p/b - b/p$
= ${12}/5 - 5/{12} = {144 - 25}/{60} = {119}/{6}$
Question : 24
What is ${cos θ}/{1 + sin θ} + 1/{cot θ}$ equal to?
a) sec θ
b) cosec θ
c) sec θ + cosec θ
d) cosec θ – cot θ
Answer »Answer: (a)
${\text"cos θ"}/{\text"1 + sin θ"} + {\text"sin θ"}/{\text"cos θ"} = {cos^2 + sin θ^2 \text"+ sin θ"}/{(\text"1 + sin θ)cos θ"}$
= $1/{\text"cos θ"}$ = sec θ
Question : 25
If tan (x + 40)° tan (x + 20)° tan (3x)° tan (70 – x)° tan (50 – x)° = 1, then the value of x is equal to
a) 20
b) 30
c) 15
d) 10
Answer »Answer: (c)
tan(x + 40)° tan (x + 20)° tan 3x° tan (70 - x)° tan (50 - x)° = 1
⇒ tan(x + 40) tan(x + 20) tan 3x cot [90 - (70 - x)] cot [90 - (50 - x)] = 1
⇒ tan(x + 40) tan (x + 20) tan 3x cot (x + 20) cot (x + 40) = 1
⇒ tan 3x = tan 45°
⇒ 3x = 45°
⇒ x = 15°
So, option (c) is correct.
IMPORTANT quantitative aptitude EXERCISES
Trigonometric Ratios & Identity Model Questions Set 1 Online Quiz
Click to Start..quantitative aptitude CATEGORIES
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »
IBPS Profit and Loss Questions Solved Problems with PDF
Most important Profit and Loss multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Aptitude MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Average Aptitude Questions Answers solutions MCQ PDF
New Average multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Quantitative Aptitude MCQ Practice Exercises all competitive exams
Continue Reading »