CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Trigonometric Identities. We need to find out the difference between square of two terms. 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 11: tan ∅ + sin ∅ = m, tan ∅ - sin ∅ = n, Find the value of m²- n²

1. 2√mn
2. 4√mn
3. m – n
4. 2mn

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Simple algebraic simplification is enough to arrive at the answer.

Adding the two equations,
tan ∅ = \\frac{(m+n)}{2}\\)
Subtracting the same,
sin ∅ = \\frac{(m-n)}{2}\\)
Since, there are no available direct formula for relation between sin∅ ∅tan∅ but we know that
cosec² ∅ – cot² ∅ = 1

∴ ((\\frac{2}{(m-n)}\\))² - ((\\frac{2}{(m+n)}\\))² = 1
=> \\frac { 4((m+n)^2 - (m-n)^2))} {((m^2-n^2))^2}\\) = 1
=>((m²-n²))² = 4(4mn)
=> m² - n² = 4√mn

The question is "To find the value of m²= n²"

Hence, the answer is 4√mn

Choice B is the correct answer.