1
Q
- The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is
(a) 1
(b) -1
(c) 0
(d) 12√
A
c)0
2
Q
If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to
(a) √3
(b) 12
(c) 12√
(d) 1
A
d)1
3
Q
- 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
A
(d) sec x = cosec y
4
Q
- sin 2B = 2 sin B is true when B is equal to
(a) 90°
(b) 60°
(c) 30°
(d) 0°
A
(d) 0°
5
Q
- If A, B and C are interior angles of a ΔABC then cos(B+C2) is equal to
a) sin A/2
b) -sin A/2
c) cos A/2
d) -cos A/2
A
a) sin A/2
6
Q
- If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to
(a) 0
(b) 13√
(c) 1
(d) √3
A
c)1
7
Q
- If y sin 45° cos 45° = tan2 45° – cos2 30°, then y = …
(a) –1/2
(b) 1/2
(c) -2
(d) 2
A
b)1/2
8
Q
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ..
(a) -1
(b) 0
(c) 1
(d) 2
A
c)1
9
Q
- 5 tan² A – 5 sec² A + 1 is equal to
(a) 6
(6) -5
(c) 1
(d) -4
A
d)-4
10
Q
- If sec A + tan A = x, then sec A =
A
x^2+1/2x
11
Q
- If sec A + tan A = x, then tan A =
A
x^2-1 /2x
12
Q
- If x = a cos 0 and y = b sin 0, then b2x2 + a2y2 =
(a) ab
(b) b² + a²
(c) a²b²
(d) a4b4
A
(c) a²b²
13
Q
- What is the maximum value of 1/csc A?
(a) 0
(b) 1
(c) 12
(d) 2
A
b)1
14
Q
- What is the minimum value of sin A, 0 ≤ A ≤ 90°
(a) -1
(b) 0
(c) 1
(d) 12
A
(b) 0
15
Q
- What is the minimum value of cos θ, 0 ≤ θ ≤ 90°
(a) -1
(b) 0
(c) 1
(d) 12
A
(b) 0
16
Q
- Given that sin θ = ab , then tan θ =
A
a/ root b^2-a^2
17
Q
- If cos 9A = sin A and 9A < 90°, then the value of tan 5A is
(a) 0
(b) 1
(c) 13√
(d) √3
A
b)1
18
Q
- If in ΔABC, ∠C = 90°, then sin (A + B) =
(a) 0
(b) 1/2
(c) 12√
(d) 1
A
d)1
19
Q
- If sin A – cos A = 0, then the value of sin4 A + cos4 A is
(a) 2
(b) 1
(c) 3/4
(d) 1/2
A
d)1/2
20
Q
- 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) 20/7
(d) 7/24
A
(b)24/7
AB=24cm and BC = 7cm
Tan C = Opposite side/Adjacent side
Tan C=24/7
21
Q
- (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:
(a) 0
(b) 1+2√3
(c) 1-√3
(d) 1+√3
A
(c)1-√3
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-√3
22
Q
- The value of tan 60°/cot 30° is equal to:
(a) 0
(b) 1
(c) 2
(d) 3
A
(b)1
Explanation: tan 60° = √3 and cot 30° = √3
Hence, tan 60°/cot 30° = √3/√3 = 1
23
Q
- 1-cos2A is equal to:
(a) sin2A
(b) tan2A
(c) 1-sin2A
(d) sec2A
A
(a)sin2A
We know, by trigonometry identities,
sin2A+cos2A = 1
1-cos2A = sin2A
24
Q
- . Sin (90° – A) and cos A are:
(a) Different
(b) Same
(c) Not related
(d) None of the above
A
(b)Same
By trigonometry identities.
Sin (90°-A) = cos A [comes in the first quadrant of unit circle]
25
26. If cos X = ⅔ then tan X is equal to:
(a) 5/2
(b) √(5/2)
(c) √5/2
(d) 2/√5
(c)√5/2
```
By trigonometry identities, we know:
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
```
26
27. If cos X=a/b, then sin X is equal to:
(a) b2-a2/b
(b) b-a/b
(c) √(b2-a2)/b
(d) √(b-a)/b
(c)√(b2-a2)/b
```
cos X=a/b
By trigonometry identities, we know that:
sin2X+cos2X=1
sin2X=1-cos2X = 1-(a/b)2
Sin X=√(b2-a2)/b
```
27
28.The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 0
(b) 1
(c) 2
(d) 4
(b)1
```
sin 60° = √3/2, sin 30° = ½, cos 60° = ½ and cos 30° = √3/2
Therefore,
√3/2 x √3/2 + ½ x ½
= 3/4 + 1/4
= 1
```
28
29. 2tan 30°/1+tan230° =
(a) Sin 60°
(b) Cos 60°
(c) Tan 60°
(d) Sin 30°
(a)Sin 60°
tan 30° = 1/√3
Putting this value we get;
2(1/√3)/1+(1/√3)2 = (2/√3)/4/3 = 6/4√3 = √3/2 = sin 60°
29
30.sin 2A = 2 sin A is true when A =
(a) 30°
(b) 45°
(c) 0°
(d) 60°
(c)0°
sin 2A = sin 0° = 0
2sin A = 2sin 0° = 0
MATHEMATICS
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