Question

sin^-1x+sin^-1y=2pi/3,then cos^-1x+cos^-1y=?

Answer 1

\[\large \sin^{-1}x + \sin^{-1}y = 2\pi/3\]

say, \(\large \sin^{-1}x = A\)
\(\large \sin^{-1}y = B\)

\[\large A + B = 2\pi/3\]

Answer 2

\(\large \sin^{-1}x = A \implies \color{red}{x = \sin A} \)

\(\large \sin^{-1}y = B \implies \color{red}{y = \sin B} \)


so,

\[\large \begin{array} \\ \cos^{-1}\color{red}{x} + \cos^{-1}\color{red}{y} &=\cos^{-1}\color{red}{\sin A} + \cos^{-1}\color{red}{\sin B} \\
&=\cos^{-1}\color{red}{\cos(\pi/2-A)} + \cos^{-1}\color{red}{\cos(\pi/2-B)} \\
&=\color{red}{(\pi/2-A)} + \color{red}{(\pi/2-B)} \\
&=\color{red}{\pi-(A+B)} \\
&=\color{red}{\pi-(2\pi/3)} \\

\end{array} \]

Answer 3

simplify^^

Answer 4

pi/3

Answer 5

oh where to study trigonometry

Answer 6

try khan :
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/inverse_trig_functions/v/inverse-trig-functions--arcsin

Answer 7

yes... thanks \(\ddot\smile\)