250+ TOP MCQs on Trigonometric Functions of Sum and Difference of Two Angles-1 & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Trigonometric Functions of Sum and Difference of Two Angles-1”.

1. cos(75°) =__________________
a) (1 – (sqrt{3}))/2(sqrt{2})
b) ((sqrt{3}) + 1)/2(sqrt{2})
c) ((sqrt{3}) – 1)/2(sqrt{2})
d) (-(sqrt{3}) – 1)/2(sqrt{2})
Answer: c
Clarification: cos(75°) = cos (45°+30°) = cos45° cos30° – sin45° sin30°
= (1/(sqrt{2}) * (sqrt{3})/2) – (1/(sqrt{2}) * 1/2) {cos(x + y)=cos x cos y – sin x sin y}
= ((sqrt{3}) – 1)/2(sqrt{2}).

2. cos(15°) =_____________
a) (1 – (sqrt{3}))/2(sqrt{2})
b) ((sqrt{3}) + 1)/2(sqrt{2})
c) ((sqrt{3}) – 1)/2(sqrt{2})
d) (-(sqrt{3}) – 1)/2(sqrt{2})
Answer: b
Clarification: cos(15°) = cos (45°-30°) = cos45° cos30° + sin45° sin30°
= (1/(sqrt{2}) * (sqrt{3})/2) + (1/(sqrt{2}) * 1/2) {cos(x – y)=cos x cos y + sin x sin y}
= ((sqrt{3}) +1)/2(sqrt{2}).

3. sin (75°) =__________________
a) (1 – (sqrt{3}))/2(sqrt{2})
b) ((sqrt{3}) + 1)/2(sqrt{2})
c) ((sqrt{3}) – 1)/2(sqrt{2})
d) (- (sqrt{3}) – 1)/2(sqrt{2})
Answer: b
Clarification: sin (75°) = sin (45°+30°) = sin45° cos30° + cos45° sin30°
= (1/(sqrt{2}) * (sqrt{3})/2) + (1/(sqrt{2}) * 1/2) {sin(x + y)=sin x cos y + cos x sin y}
= ((sqrt{3}) + 1)/2(sqrt{2}).

4. sin(15°) =_________________
a) (1 – (sqrt{3}))/2(sqrt{2})
b) ((sqrt{3}) + 1)/2(sqrt{2})
c) ((sqrt{3}) – 1)/2(sqrt{2})
d) (- (sqrt{3}) – 1)/2(sqrt{2})
Answer: c
Clarification: sin (15°) = sin (45°-30°) = sin45° cos30° – cos45° sin30°
= (1/(sqrt{2}) * (sqrt{3})/2) – (1/(sqrt{2}) * 1/2) {sin(x – y)=sin x cos y – cos x sin y}
= ((sqrt{3}) -1)/2(sqrt{2}).

5. Is cos (90° – x) = sin x.
a) True
b) False
Answer: a
Clarification: cos (90° – x) = cos 90° cos x + sin 90° sin x {cos(x – y)=cos x cos y + sin x sin y}
= 0*cos x + 1*sin x
= sin x.

6. Is sin (90°+x) = cos x.
a) True
b) False
Answer: a
Clarification: sin (90°+x) = sin 90° cos x + cos 90° sin x {sin(x + y)=sin x cos y + cos x sin y}
= 1*cos x + 0*sin x
= cos x.

7. tan(75°) =___________________
a) 2+(sqrt{3})
b) 2-(sqrt{3})
c) 1+(sqrt{3})
d) (sqrt{3})-1
Answer: a
Clarification: tan (x +y) = (tan x + tan y)/(1- tan x tan y)
tan (45°+30°) = (tan 45° + tan 30°)/(1- tan 45° tan 30°)
tan 75° = (1+ 1/(sqrt{3}))/(1-1/(sqrt{3})) = ((sqrt{3}) + 1)/ ((sqrt{3}) – 1) = 2+(sqrt{3}).

8. tan(15°) =___________________
a) 2 + (sqrt{3})
b) 2 – (sqrt{3})
c) 1 + (sqrt{3})
d) (sqrt{3}) – 1
Answer: b
Clarification: We know, tan (x -y) = (tan x – tan y)/(1+ tan x tan y)
tan (45°-30°) = (tan 45° – tan 30°)/(1+ tan 45° tan 30°)
tan 75° = (1- 1/(sqrt{3}))/ (1+ 1/(sqrt{3})) = ((sqrt{3}) – 1)/ ((sqrt{3}) + 1) = 2-(sqrt{3}).

9. cot 75° =___________________________
a) 2+(sqrt{3})
b) 2-(sqrt{3})
c) 1+(sqrt{3})
d) (sqrt{3})-1
Answer: b
Clarification: We know, cot (x +y) = (cot x cot y -1)/(cot y + cot x)
cot(45°+30°) = (cot 45° cot 30°-1)/(cot 45° + cot 30°)
cot 75° = ((sqrt{3}) – 1)/((sqrt{3}) + 1) = 2-(sqrt{3}).

10. cot 15° =______________
a) 2+(sqrt{3})
b) 2-(sqrt{3})
c) 1+(sqrt{3})
d) (sqrt{3})-1
Answer: a
Clarification: We know, cot (x – y) = (cot x cot y +1)/cot y – cot x)
cot(45°-30°) = (cot 45° cot 30°+1)/(cot 45° – cot 30°)
cot 15° = ((sqrt{3}) + 1)/((sqrt{3}) – 1) = 2+(sqrt{3}).

11. Find cos 2x if sin x=1/2.
a) 1/2
b) 1/(sqrt{2})
c) (sqrt{3})/2
d) 1
Answer: c
Clarification: We know, cos 2x = cos²x – sin²x = 1-2sin²x {cos²x = 1-sin²x}
= 1-2(1/2)² = 1-2(1/4) = 1-1/2 = 1/2.

12. Find cos 2x if cos x = 1/(sqrt{2}).
a) 1/2
b) 0
c) (sqrt{3})/2
d) 1
Answer: b
Clarification: We know, cos 2x = cos²x – sin²x = 2cos²x – 1 {sin²x = 1-cos²x}
= 2(1/(sqrt{2}))²-1 = 2(1/2) – 1 = 1-1 = 0.

13. Find cos 2x if tan x=1/(sqrt{3}).
a) 1/2
b) 0
c) (sqrt{3})/2
d) 1
Answer: a
Clarification: We know, cos 2x = cos²x – sin²x = (cos²x – sin²x)/(cos²x+sin²x) {1 = sin²x + cos²x}
= (1-tan²x)/(1+tan²x)
= (1-(1/(sqrt{3}))²)/(1+(1/(sqrt{3}))²)
= (1-1/3)/(1+1/3) = (2/3)/(4/3) = 1/2.