in this question how did sin^{-1}v appear?shouldn't it be cos^{-1}v?(Underlined part)

in this question how did sin-1v appear?shouldn't it be cos-1v?(Underlined part) lfu=sü-t x), prate that —
SOL.CTTON We have,
u (m ccs¯ x) x)
sin¯ u —m cs- x and as - x
sin¯ u •sin¯ v =m(cos¯ x + sin¯ x)
Ehfferentiatirtg both sides with respect to v, we chtain