Mathematics Questions and Answers – Trigonometric Functions of Sum and Difference of Two Angles-1

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This set of Mathematics 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\(\sqrt{2}\).
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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\(\sqrt{2}\).
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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+\(\sqrt{3}\).
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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-\(\sqrt{3}\).
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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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter