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 : 6
If the given figure, BC = 15 cm and sin B = $4/5$. What is the value of AB?
a) 20 cm
b) 25 cm
c) 5 cm
d) 4 cm
Answer »Answer: (b)
BC = 15 cm and sin B = $4/5$
sin B = ${AC}/{AB} = 4/5$
then BC = 3m
But, BC = 15 (given)
then AC = 4 × 5 = 20
AB = 5 × 5 = 25.
Hence, the value of AB is 25 cm.
Question : 7
If tan θ + sec θ = 2, then tan θ is equal to
a) $5/4$
b) $3/4$
c) $3/2$
d) $5/2$
Answer »Answer: (b)
tan θ + sec θ = 2 ......(i)
As we know
⇒ $sec^2 θ - tan^2 θ$ = 1
⇒ (sec θ - tan θ)(sec θ + tan θ) = 1
⇒ sec θ - tan θ = $1/2$ ....(ii)
equation (i) - eq (ii)-
2 tan θ = 2 - 1/2
2 tan θ = $3/2 ⇒ tan θ = 3/4$
So, option (b) is correct.
Question : 8
If sec x cosec x = 2, then what is $tan^n x + cot^n$ x equal to?
a) $2^{n + 1}$
b) 2
c) 2n
d) $2^{n – 1}$
Answer »Answer: (b)
sec x cosec x = 2
This value is possible is x = 45°
$tan^n x + cot^n x = (\text"tan x")^n + (\text"cot x")^n$
= $(tan 45°)^n + (cot 45°)^n = (1)^n + (1)^n = 2$
Question : 9
If α is the angle of first quadrant such that $cosec^4 α = 17 + cot^4$ α, then what is the value of sin α?
a) $1/4$
b) $1/3$
c) $1/9$
d) $1/{16}$
Answer »Answer: (b)
$cosec^4 α - cot^4$ α = 17 (Given)
⇒ $(cosec^2 α - cot^2 α) (cosec^2 α + cot^2 α)$ = 17
⇒ 1.$({1 + cos^2 α}/{sin^2 α})$ = 17
⇒ 2 - $sin^2 α = 17 sin^2 α$
⇒ $18 sin^2 α = 2 ⇒ sin^2 α = 1/9$
∴ sin α = $1/3$ (since, α lie in first quadrant)
Question : 10
If p = $√{{1 - \text"sin x"}/{1 + \text"sin x"}}, q = {1 - \text"sin x"}/{\text"cos x"}, r = {\text"cos x"}/{1 + \text"sin x"}$
then which of the following is/are correct ?
1. p = q = r
2. $p^2$ = qr
Select the correct answer using the code given below.
a) 2 only
b) 1 only
c) Both 1 and 2
d) Neither 1 nor 2
Answer »Answer: (c)
Statement 1
1 = ${√{\text"1 - sin n"}}/{√{\text"1 + sin x"}} = √{{(\text"1 - sin x")(\text"1 - sin x")}/{(\text"1 - sin x")(\text"1 + sin x")}}$
= ${\text"1 - sin x"}/{√{1 - sin^2 x}} = {\text"1 - sin x"}/{√{cos^2 x}} = {\text"1 - sin x"}/{\text"cos x"}$
P = q
r = ${\text"cos x"}/{\text"1 + sin x"} = {\text"cos x" (\text"1 - sin x")}/{(\text"1 + sin x")(\text"1 - sin x")} = {\text"cos x" (\text"1 - sin x")}/{1 - sin^2 x}$
= ${\text"cos x" (\text"1 - sin x")}/{cos^2 x} = {\text"1 - sin x"}/{\text"cos x"}$
P = q = r
Now,
Statement 2
$p^2$ = qr
= ${\text"1 - sin x"}/{\text"cos x"} . {\text"cos x"}/{\text"1 + sin x"} = {\text"1 - sin x"}/{\text"1 + sin x"} = P^2$
So, Both are correct.
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