interesting one

Geometry Level 1

$If\quad \sin { (x) } +\quad \csc { (x) } \quad =\quad 2,\\ What\quad is\quad the\quad value\quad of\\ \sin ^{ 2 }{ (x) } +\csc ^{ 2 }{ (x) } ?$

2 solutions

Tay Yong Qiang
Aug 18, 2015

$\sin x + \csc x=2$

$(\sin x + \csc x)^2 = 2^2$

$\sin ^2 x + \csc ^2 x + 2\sin x \csc x=4$

$\sin ^2 x + \csc ^2 x =4-2=\boxed{2}$

Parth Panchal
Apr 23, 2015

Here Sin(x) + cosec(x) = 2 , Thus the value of x is pie/2 on unit circle SO substituting x=pie/2 in equation below the equation is 1+1=2