NCERT Solutions for class 11 Maths | Chapter 3 - Trigonometric Functions

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Questions
1 In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals
A none of these
B c/a
C 1
D a/c

Answer:1
2 The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is
A 30°
B 90°
C 60°
D 120°

Answer:90°
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3 If cos a + 2cos b + cos c = 2 then a, b, c are in
A 2b = a + c
B b² = a × c
C a = b = c
D None of these

Answer:2b = a + c
4 If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is
A x + y
B 1/x + y
C x + 1/y
D 1/x + 1/y

Answer:1/x + 1/y
5 If cos a + 2cos b + cos c = 2 then a, b, c are in
A 2b = a + c
B b² = a × c
C a = b = c
D None of these

Answer: 2b = a + c
6 The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is
A sin x
B sin 2x
C sin 3x
D sin 4x

Answer:sin 3x
7 The value of cos 20 + 2sin² 55 – √2 sin65 is
A 0
B 1
C -1
D None of these

Answer:1
8 If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is
A 4 : (√5 – 1)
B 5 : 4
C (√5 – 1) : 4
D none of these

Answer:4 : (√5 – 1)
9 If 3 × tan(x – 15) = tan(x + 15), then the value of x is
A 30
B 45
C 60
D 90

Answer:45
10 The value of cos 5π is
A 0
B 1
C -1
D None of these

Answer:-1
11 The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is
A sin (x + y)
B sin² (x + y)
C sin³ (x + y)
D sin4 (x + y)

Answer:sin² (x + y)
12 The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is
A tan 6x
B 2 tan 6x
C 3 tan 6x
D 4 tan 6x

Answer:2 tan 6x
13 The value of tan 20 × tan 40 × tan 80 is
A tan 30
B tan 60
C 2 tan 30
D 2 tan 60

Answer:tan 60
14 If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is
A 4 : (√5 – 1)
B 5 : 4
C (√5 – 1) : 4
D none of these

Answer:4 : (√5 – 1)
15 If a×cos x + b × cos x = c, then the value of (a × sin x – b²cos x)² is
A a² + b² + c²
B a² – b² – c²
C a² – b² + c²
D a² + b² – c²

Answer: a² + b² – c²
16 The value of cos 180° is
A 0
B 1
C -1
D infinite

Answer:-1
17 If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is
A π/3
B π/2
C 2π/3
D 3π/2

Answer:2π/3
18 The general solution of √3 cos x – sin x = 1 is
A x = n × π + (-1)n × (π/6)
B x = π/3 – n × π + (-1)n × (π/6)
C x = π/3 + n × π + (-1)n × (π/6)
D x = π/3 – n × π + (π/6)

Answer:x = π/3 + n × π + (-1)n × (π/6)
19 If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is
A 2 – e²
B (2 – e²)1/2
C (2 – e²)²
D (2 – e²)3/2

Answer: (2 – e²)3/2
20 If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is
A 2π/3
B π/3
C π/2
D π/6

Answer: 2π/3

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