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 : 16
What is sin 25° sin 35° sec 65° sec 55° equal to?
a) 0
b) –1
c) $1/2$
d) 1
Answer »Answer: (d)
sin 25° sin 35° sec 65° sec 55°
= sin 25° . sin 35° . $1/{cos 65°} . 1/{cos 55°}$
= sin 25° . sin 35° . $1/{cos (90 - 25°)} . 1/{cos (90 - 35°)}$
= sin 25° . sin 35° . $1/{sin 25°} . 1/{sin 35°}$ = 1
Question : 17
If $sin^2$ x + sin x = 1, then what is the value of $cos^{12} x + 3 cosx^{10} x + 3 cos^8 x + cosx^6$ x?
a) 0
b) &1
c) 1
d) 8
Answer »Answer: (c)
We have,
$sin^2x$ + sin x = 1...(1)
∴ sin x = 1 - $sin^2 x = cos^2 x$
On cubing equation (1), we get
$(sin^2 x + sin x)^3 = {1}^3$
$sin^6 x + sin^3 x + 3 sin^2 x. sin x (sin^2 \text"x + sin x")$ = 1
$sin^6x + sin^3 x + 3 sin^5x + 3 sin^4x$ = 1
∴ $cos^{12}x + 3 cos^{10}x + 3 cos^8 x + co^6 x$ = 1
Question : 18
If from the top of a post a string twice the length of the post is stretched tight to a point on the ground, then what angle will the string make with the post?
a) ${π}/4$
b) ${π}/6$
c) ${5 π}/{12}$
d) ${π}/3$
Answer »Answer: (d)
Let AB be the height, AC be the string and the angle made by string with the post be θ.
From figure cos θ = ${AB}/{AC} = h/{2h} = 1/2 = cos {π}/3$
θ = ${π}/3$
Question : 19
If $cos^2$ x + cosx = 1, then what is the value of $sin^{12}x + 3sin^{l0}x + 3sin^8 x +sin^6$ x
a) 2
b) 1
c) 4
d) 8
Answer »Answer: (b)
$cos^2 \text"x + cos x = 1"$
⇒ $\text"cos x = 1" - cos^2 x = sin^2 x$
= $sin^{12}x + 3 sin^{10}x + 3 sin^8x + sin^6x$
= $sin^6x[sin^6x + 3 sin^4x + 3 sin^2 x + 1]$
= $sin^6x[sin^2 x + 1]^3$
= $[sin^4x + sin^2 x]^3$
$(∴ sin^4 x = cos^2 x)$
= $(sin^2 x + cos^2 x)$ = 1
Question : 20
If 5 sin θ + 12 cos θ = 13, then what is 5 cos θ – 12 sin θ equal to?
a) –1
b) –2
c) 0
d) 1
Answer »Answer: (c)
∵ 5 sin θ + 12 cos θ = 12
Now, squaring both sides, we get
$25 sin^2 θ + 144 cos^2 θ + \text"120 sin θ cos θ"$ = 169
⇒ 25$(1 - cos^2 θ) + 144(1 - sin^2 θ) + \text"120 sin θ cos θ"$ = 169
⇒ 25 - 25 $ cos^2 θ + 144 - 144 sin^2 θ + \text"120 sin θ cos θ"$ - 169
⇒ 25 $cos^2 θ + 144 sin^2 θ - \text"120 sin θ cos θ" = 169 - 169$
⇒ $(\text"5 cos θ - 12 sin θ")^2$ = 0
∴ 5 cos θ - 12 sin θ = 0
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
Most Important Antonyms Vocabulary - IBPS Clerk Prelims 2024
Latest Antonyms multiple choice questions and answers with free PDFfor IBPS Clerk Prelims 2024. English Vocabulary practice exercise for all bank exam
Continue Reading »
Syllogism Practice Questions Answers PDF - IBPS Clerk 2024
Practice Verbal Reasoning Syllogism multiple choice questions and answers with Fully solved explanation, PDF for the IBPS Clerk Prelims 2024 Bank Exam
Continue Reading »
IBPS Clerk Prelims 2024 Synonyms Questions Solved Answers
Most important IBPS Clerk Prelims 2024 Synonyms and Antonyms multiple choice questions and answers with detailed solutions, English vocabulary PDF Download
Continue Reading »
New Cloze Test Questions and Answers PDF - IBPS Clerk 2024
The most important Cloze Test questions with detailed answers for upcoming IBPS Clerk prelims 2024. Latest English verbal ability practice MCQs, PDF
Continue Reading »