Answer the following questions.

MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Answer the following questions. (i) Prove that for any real numbers

a

and

b

in the open interval

(0,1)

\arcsin a+\arccos b=\frac{\pi}{2}

if and only if

a=b

. (ii) Hence, without direct evaluation, decide whether

\arcsin(0.6)+\arccos(0.7)

is less than, equal to, or greater than

\frac{\pi}{2}

. Give reasons for the conclusion.