Trigonometry- MCQ Test 1

1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:

A) 12/7
B) 24/7
C) 16/7
D) 18/7

ANSWER=> (B)
Explanation/Answer:-
AB = 24 cm and BC = 7 cm
tan C = perpendicular / base tan C = 24/7

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2. (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:

A) 0
B) 1
C) 1-√3
D) 1+√3

ANSWER=> (C)

sin 30° = ½, sin 60° = √3/2, cos 30° = √3/2 and cos 60° = ½
Putting these values, we get:
(½+½)-(√3/2+√3/2)
= 1 – [(2√3)/2]
= 1 – √3

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3. 1 – cos²A is equal to:

A) 1+sin²A
B) sin²A
C) tan²A
D) cos²A

ANSWER=> (B)
Explanation/Answer:-
1 – cos²A=sin²A

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4. If cos X = ⅔ then tan X is equal to:

A) 5/2
B) √(5/2)
C) √5/2
D) 2/√5

ANSWER=> (C)
Explanation/Answer:-
1 + tan²X = sec²X
And sec X = 1/cos X = 1/(⅔) = 3/2
Hence,
1 + tan²X = (3/2)² = 9/4
tan²X = (9/4) – 1 = 5/4
tan X = √5/2

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5. sin 2A = 2 sin A is true when A =

A) 30°
B) 45°
C) 0°
D) 90°

ANSWER=> (C)
Explanation/Answer:-sin 2A = 2 sin A
=> 2sinAcosA = 2 sin A
=> sinAcosA = sin A
=> cosA = 1
=> cosA = cos0°
=> A = 0°

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6. The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is

A) 1/√2
B) 1
C) 0
D) -1

ANSWER=> (C)
Explanation/Answer:- cos 0°. cos 1°. cos 2°. cos 3°… cos 89°. cos 90°
cos 90°=0

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7. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to

A) √3
B) 1/2
C) 1/√2
D) 1

ANSWER=> (D)
Explanation/Answer:- x tan 45° sin 30° = cos 30° tan 30°
Put tan 45°=1, sin 30°=1/√2,cos 30°=√3/2 tan 30°=1/√3

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8. If x and y are complementary angles, then

A) sin x = sin y
B) tan x = tan y
C) cos x = cos y
D) sec x = cosec y

ANSWER= (D)
Explanation/Answer:- If x and y are complementary angles, then X=90-Y
sec x=sec(90-Y)= cosec y

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9. If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to

A) 0
B) 1/√3
C) 1
D) √3

ANSWER= (C)
Explanation/Answer:- sin A = cos (2A – 45°)
cos(90°- A )= cos(2A – 45°)
(90°- A )= (2A – 45°)
3A = 135°
A = 45°
tan 45°=1

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10. If sin θ + sin² θ = 1, then cos² θ + cos^4 θ = ..

A) -1
B) 0
C) 1
D) 2

ANSWER= (C)
Explanation/Answer:- Given, sin θ + sin² θ = 1
=> sin θ = 1 - sin² θ = cos² θ
Now, putting valuse of cos² θ in cos² θ + cos^4 θ
=> sin θ + sin² θ
So, the solution of cos² θ + cos^4 θ is 1.