The question is from CAT Geometry - Trigonometry. This is about Trigonometric Identities. Our task is to find out the value of the term which is in a, b, c, d. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 5: : If cos A + cos^{2} A = 1 and a sin^{12} A + b sin^{10} A + c sin^{8} A + d sin^{6} A - 1 = 0. Find the value of a+b/c+d

- 4
- 3
- 6
- 1

3

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Given,

Cos A = 1 - Cos^{2}A

=> Cos A = Sin^{2} A

=> Cos^{2}A = Sin^{4}A

=> 1 – Sin^{2} A = Sin^{4} A

=> 1 = Sin^{4} A + Sin^{2} A

=> 1^{3} = (Sin^{4}A + Sin^{2}A)^{3}

=> 1 = Sin^{12} A + Sin^{6}A + 3Sin^{8} A + 3Sin^{10} A

=> Sin^{12} A + Sin^{6}A + 3Sin^{8} A + 3Sin^{10} A – 1 = 0

On comparing,

a = 1, b = 3 , c = 3 , d = 1

∴ \\frac{b}{c}\\) + d = 3

Always look out for Pythagorean triplets, we know that (8,15,17) is one

∴ 17 (\\frac{18}{7}\\)CosA+\\frac{15}{17}\\)SinA)

The question is **"Find the value of a+b/c+d"**

Choice B is the correct answer.

CAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

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

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

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