Your cart is empty.
Practice each question, then open the answer or worked solution.
If f(x) = cos2x + sec2x, then
A. f(x) < 1
B. f(x) = 1
C. 2 < f(x) < 1
D. f(x) ≥ 2
[Hint: A.M ≥ G.M.]
D. f(x) ≥ 2
Explanation:
According to the question,
We have, f(x) = cos2x + sec2x
We know that, A.M ≥ G.M.
⇒ cos02x + sec2x ≥ 2
⇒ f(x) ≥ 2
Thus, option (D) f(x) ≥ 2 is the correct answer.
If tan θ = 1/2 and tan ϕ = 1/3, then the value of θ + ϕ is
A. π/6
B. π
C. 0
D. π/4
D. π/4
Explanation:
According to the question,
Thus, option (D) π/4 is the correct answer.
Which of the following is not correct?
A. sin θ = – 1/5
B. cos θ = 1
C. sec θ = ½
D. tan θ = 20
C. sec θ = ½
Explanation:
According to the question,
We know that,
a) sin θ = – 1/5 is correct since Sin θ ∈ [-1,1]
b) cos θ = 1 is correct since Cos θ ∈ [-1,1]
c) sec θ = ½
⇒ (1/cos θ) = ½
⇒cos θ=2 is incorrect since Cos θ ∈ [-1,1]
d) tan θ = 20 is correct since tan θ ∈ R.
Thus, option (C) sec θ = ½ is the correct answer.
The value of tan 1° tan 2° tan 3°… tan 89° is
A. 0
B. 1
C. ½
D. Not defined
B. 1
Explanation:
According to the question,
tan 1° tan 2° tan 3°… tan 89°
= tan 1° tan 2° … tan 45° tan (90-44°) tan(90-43°)…tan (90-1°)
= tan 1°tan 2° … tan 45°cot 44°cot 43°…cot 1° [∵tan (90-θ)=cot θ]
= tan 1° cot 1° tan 2° cot 2°…tan45°… tan 89° cot 89°
=1.1….1 = 1
Thus, option (B) 1 is the correct answer.
The value of (1 – tan215o)/(1 + tan215o) is
A. 1
B. √3
C. √3/2
D. 2
C. √3/2
Explanation:
According to the question,
Let θ = 15° ⇒ 2θ = 30°
Now, since we know that,
Thus, option (C) √3/2 is the correct answer.
The value of cos 1° cos 2° cos 3°… cos 179° is
A. 1/√2
B. 0
C. 1
D. –1
B. 0
Explanation:
According to the question,
Since cos90° =0
We get,
⇒ cos 1° cos 2° cos 3°… cos90°… cos 179° = 0
Thus, option (B) 0 is the correct answer.
If tan θ = 3 and θ lies in third quadrant, then the value of sin θ is
A. 1/√10
B. – 1/√10
C. – 3/√10
D. 3/√10
C. – 3/√10
Explanation:
According to the question,
Given that, tan θ = 3 and θ lies in third quadrant
⇒ cot θ = 1/3
We know that,
Cosec2θ = 1+cot2θ
Thus, option (C) – 3/√10 is the correct answer.
The value of tan 75°– cot 75° is equal to
A. 2√3
B. 2 + √3
C. 2 – √3
D. 1
A. 2√3
Explanation:
According to the question,
We have,
tan 75°– cot 75°
= -2cot150°
= -2 cot (180°-30°)
= 2cot30°
=2√3
Thus, option (A) 2√3 is the correct answer.