Sum and Difference of Two Angles - Class 11 Maths MCQ

This set of Class 11 Maths Chapter 3 Multiple Choice Questions & Answers (MCQs) focuses 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\(\sqrt{2}\)
View Answer

Answer: c
Explanation: 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\(\sqrt{2}\)
View Answer

Answer: b
Explanation: 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\(\sqrt{2}\)
View Answer

Answer: b
Explanation: 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\(\sqrt{2}\)
View Answer

Answer: c
Explanation: 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
View Answer

Answer: a
Explanation: 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.

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6. Is sin (90°+x) = cos x.
a) True
b) False
View Answer

Answer: a
Explanation: 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
View Answer

Answer: a
Explanation: 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
View Answer

Answer: b
Explanation: 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
View Answer

Answer: b
Explanation: 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
View Answer

Answer: a
Explanation: 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
View Answer

Answer: c
Explanation: 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
View Answer

Answer: b
Explanation: 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
View Answer

Answer: a
Explanation: 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.

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