CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

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 + cos² A = 1 and a sin¹² A + b sin¹⁰ A + c sin⁸ A + d sin⁶ A - 1 = 0. Find the value of a+b/c+d

1. 4
2. 3
3. 6
4. 1

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Can we use pythagorean triplets here? Think!!

Given,
Cos A = 1 - Cos²A
=> Cos A = Sin² A
=> Cos²A = Sin⁴A
=> 1 – Sin² A = Sin⁴ A
=> 1 = Sin⁴ A + Sin² A
=> 1³ = (Sin⁴A + Sin²A)³

=> 1 = Sin¹² A + Sin⁶A + 3Sin⁸ A + 3Sin¹⁰ A
=> Sin¹² A + Sin⁶A + 3Sin⁸ A + 3Sin¹⁰ 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"

Hence, the answer is 3

Choice B is the correct answer.