Let sin t a cos t b and tan t c Write the expression in te

Let sin t = a. cos t = b. and tan t =c Write the expression in terms of a, b, and c. sin(t + 8x)- cos(t + 6x) + tan(t + 7 x) sin (t + 8x) - cos (t + 6x) + tan (t + 7x)

Solution

sin(t + 8pi) - cos(t +6pi) + tan(t +7pi)

sin(t + 8pi) = sint { sin (x +2pi*n) = sinx}

cos( t +6pi) = cost   { cos(x +2pi*n) = cosx}

tan(t +7pi) = tanx   { tan (x +pi*n) = sinx}

So, sin(t + 8pi) - cos(t +6pi) + tan(t +7pi)

= sint - cost + tant

= a - b + c