Question

What is the value of 5 \(cos^{-1}\frac{⁡1}{2} + 7 sin^{-1}⁡(\frac{-1}{2})\) ?

(a) –\(\frac{π}{2}\)

(b) π

(c) \(\frac{π}{2}\)

(d) \(\frac{17π}{6}\)

The question was asked in a national level competition.

The question is from Inverse Trigonometric Functions Basics topic in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Right choice is (c) \(\frac{π}{2}\)

To explain: \(cos^{-1}⁡(\frac{⁡1}{2})=\frac{π}{3} and sin^{-1}⁡(-\frac{⁡1}{2})=-\frac{π}{6}\)

∴ 5 \(cos^{-1}⁡\frac{1}{2}+7 sin^{-1}⁡(-\frac{1}{2}) =5(\frac{π}{3})+7(-\frac{π}{6})\)

=\(\frac{5π}{3}-\frac{7π}{6}=\frac{10π-7π}{6}=\frac{3π}{6}=\frac{π}{2}\)