IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: **IPM Sample Paper**

Question 36 : Given that cos x + cos y = 1, the range of sin x - sin y is

- [-1, 1]
- [-2, 2]
- [0, √3]
- [-√3, √3]

[-√3, √3]

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Let’s say sin x – sin y = k. So we intend to find the range of k.

We have cos x + cos y = 1

So, k^{2} + 1^{2} = (sin x - sin y )^{2} + (cos x + cosy )^{2}

k^{2} + 1^{2} = (sin x)^{2} + (sin y)^{2} – 2(sin x)(sin y) + (cos x)^{2} + (cos y)^{2} + 2(cos x)(cos y)

k^{2} + 1^{2}= sin^{2} x + cos^{2} x + sin^{2} y + cos^{2} y + 2(cos x)(cos y) – 2(sin x)(sin y)

k^{2} + 1^{2} = 1 + 1 + 2(cos x)(cos y) – 2(sin x)(sin y) {Because, sin^{2} x + cos^{2} x = 1}

k^{2} + 1^{2}= 2 + 2[(cos x)(cos y) – (sin x)(sin y)] {Because, (cos x)(cos y) – (sin x)(sin y) = cos(x + y)}

k^{2} = 1 + 2(cos(x + y))

The maximum value that a cos function can take is 1, and the minimum value is -1.

Therefore the maximum value that k^{2} can take is 1+2(1) = 3,

and the minimum value that k^{2} can take is 1+2(-1) = -1,

This is impossible, k^{2} is always non-negative.

The minimum value that k^{2} can take is 0.

Therefore (k^{2})_{max} = 3 and (k^{2})_{min} = 0.

To get the range of k, we concentrate on (k^{2})_{max}.

(k^{2})_{max} = 3, implies that the extreme values of k are:

k = +√3 or -√3

So, the values of k range between +√3 and -√3, both +√3 and -√3 inclusive.

k = sin x – sin y, Remember!!

Therefore, Range of sin x – sin y = [-√3, √3]

The question is **"Given that cos x + cos y = 1, the range of sin x - sin y is" **

Choice D is the correct answer

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com