Exams › SSC CGL (Prelims) › General

If a*sin^3(x) + b*cos^3(x) = sin(x)*cos(x) and a*sin(x) = b*cos(x), find a^2 + b^2 (given x is neither 0 nor 90 degrees).

1. a^2 - b^2
2. 1
3. 0
4. a^2 + b^2

Correct answer: 1

Solution

From a*sin(x) = b*cos(x): sin(x)/cos(x) = b/a => tan(x) = b/a. So sin(x) = b/sqrt(a^2+b^2), cos(x) = a/sqrt(a^2+b^2). Substitute into first equation: the equation reduces to 1/(a^2+b^2) = 1/(a^2+b^2) only when a^2+b^2 = 1.

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