simplify the following expression sint8piesect5pietant9pieco

simplify the following expression
sin(-t+8pie)sec(t+5pie)/tan(t+9pie)cot(-t-5pie)

Solution

[ sin( - t +8pi)sec(t +5pi) ]/[ tan(t +9pi)cot(-t - 5pi) ]

As per trigonometric identities : sin(x +2k*pi) = sinx ; cos(x + 5pi) = cos(x+pi) = -cosx ;

tan(x+ 9pi) = tanx ; cot(-x) = -cotx ; cos(x+ 5pi) = cotx

So, [ sin( - t +8pi)sec(t +5pi) ]/[ tan(t +9pi)cot(-t - 5pi) ]

= [ sin(-t)(-sect)]/[tant*(-cot)]

= (sint/cos^2t)/ (-1)

= -tant*sect