Trigonometric Ratios & Identity Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Trigonometric Ratios & Identities topic of quantitative aptitude
- ${cos 75°}/{sin 15 °} + {sin 12°}/{cos 78°} - {cos 18°}/{sin 72°}$ = 1
- ${cos 35°}/{sin 55°} - {sin 11°}/{cos 79°}$ + cos 28° cosec 62°= l
- ${sin 80°}/{cos 10°}$ - sin 59° sec 31° = 0
(a) 2 and 3 only
(b) 1 and 2 only
(c) 1 and 3 only
(d) 1, 2 and 3
The correct answers to the above question in:
Answer: (d)
1. ${cos 75°}/{sin 15°} + {sin 12°}/{cos 78°} - {cos 18°}/{sin 72°}$ = 1
${cos 75°}/{cos 75°} + {sin 12°}/{sin 12°} - {cos 18°}/{cos 18°}$ = 1
2 - 1 = 1
Statement is correct.
2. ${cos 35°}/{sin 55°} - {sin 11°}/{cos 79°}$ + cos 28° cosec 62° = 1
${cos 35°}/{cos 35°} - {sin 11°}/{sin 11°}$ + cos 28° sec 28° = 1
1 - 1 + 1 = 1
2nd Statement is also true.
3. ${sin 80°}/{cos 10°}$ - sin 59° sec 31° = 0
${sin 80°}/{sin 80°}$ - sin 59° cosec 59° = 0
1 - 1 = 0
3rd Statement is correct.
Practice Trigonometric Ratios & Identities (Trigonometric Ratios & Identity Model Questions Set 1) Online Quiz
Discuss Form
Read more model questions set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
If cos A = tan B, cos B = tan C and cos C = tan A then sin A is equal to
a) ${√5 - 1}/2$
b) ${√5 - 1}/4$
c) ${√3 - 1}/4$
d) None of these
Answer »Answer: (d)
Cos A = tan B
Squaring on both sides
$cos^2 A = tan^2 B$
⇒ $tan^2 B = {sin^2 B}/{cos^2 B} = {1 - cos^2 B}/{cos^2 B}$
∴ $cos^2 A = {1 - cos^2 B}/{cos^2 B}$
$cos^2 A = {1 - tan^2 C}/{tan^2 C}$
(∵ cos B = tan C)
⇒ $cos^2 A tan^2 C = 1 - tan^2 C = 1 - {sin^2 C}/{cos^2 C} $
⇒ $cos^2 A {sin^2 C}/{cos^2 C} ={cos^2 C - sin^2 C}/{cos^2 C}$
⇒ $cos^2 A (1 - cos^2 C) = 2 cos^2 C - 1$
⇒ $cos^2 A (1 - tan^2 A) = 2 tan^2 A - 1$
$cos^2 A - sin^2 A = {2 sin^2 A}/{cos^2 A} - 1$
⇒ 1 - $2sin^2 A = {2 sin^2 A - cos^2 A}/{cos^2 A}$
⇒ $cos^2 A (1 - sin^2 A) = 2 sin^2 A - cos^2 A$
⇒ $cos^2 A (1 - 2 sin^2 A) = 2 sin^2 A - 1 + sin^2 A$
⇒ $(1 - sin^2 A) (1 - 2 sin^2 A) = 3 sin^2 A - 1$
⇒ $1 - 2 sin^2 A - sin^2 A + 2 sin^4A = 3 sin^2 A - 1$
⇒ $1 - 3 sin^2 A + 2 sin^4 A = 3 sin^2 A - 1$
⇒ $2 sin^4 A - 6 sin^2 A + 2 = 0$
⇒ $sin^4 A - 3 sin^2$ A + 1 = 0
This is quadratic equation in $sin^2$ A
$(sin^2 A)^2 - 3 (sin^2 A) + 1 = 0$
$sin^2 A = {3 ± √{(- 3)^2 - 4 (1) (1)}}/2$
= ${3 ± √5}/2$
$sin^2 A = {3 + √5}/2$ not possible because $sin^2 A$ ≯ 1
So $sin^2 A = {3 - √5}/2$
So none of the options are correct.
Question : 2
If sin θ + cos θ = 1, then what is the value of sin θ cos θ ?
a) 0
b) 2
c) 1
d) $1/2$
Answer »Answer: (a)
Given, $\text"sin θ + cos θ"$ = 1
Squaring both sides,
$(sin^2 θ + cos^2 θ) + 2 \text"sin θ cos θ" = 1$
⇒ 1 + 2 sin θ cos θ = 1 ⇒ sin θ cos θ = 0.
Question : 3
If 0 ≤ θ ≤ ${π}/2$ and cos θ + $√3$ sin θ = 2, then what is the value of θ ?
a) ${π}/4$
b) ${π}/3$
c) ${π}/6$
d) ${π}/2$
Answer »Answer: (b)
Given that, cos θ + $√3$ sin θ = 2
⇒ $1/2 cos θ + {√3}/2$ sin θ = 1
⇒ sin 30° cos θ + cos 30° sin θ = 1
⇒ sin(30° + θ) = sin 90°
30° + θ = 90°
∴ θ = 60°
GET Trigonometric Ratios & Identities PRACTICE TEST EXERCISES
Trigonometric Ratios & Identity Model Questions Set 1
Trigonometric Ratios & Identities Shortcuts and Techniques with Examples
Verbal Reasoning
Question & Answer Quiz
Non Verbal Reasoning
Question & Answer Quiz
Quantitative Aptitude
Question & Answer Quiz
Computer MCQ
Question & Answer Quiz
General English
Question & Answer Quiz
History GK
Question & Answer Quiz
Polity GK
Question & Answer Quiz
Geography GK
Question & Answer Quiz
Economy GK
Question & Answer Quiz
General Awareness GK
Question & Answer Quiz
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 »