Question

If sinq = cotq, then the value of (cos^2q + 2cos^3q + cos^4q -3) is

Answer 1

sinq = cotq
sinq = cosq/sinq
sin^2 q= cosq
1 - cos^2 q = cosq
cos^2 q = 1 -cosq

then cos^2q + 2cos^3q + cos^4q -3
= cos^2 q(1 + 2cosq + cos^2 q) - 3
= (1 - cosq)(1 + cosq)^2 - 3
= (1 - cos^2 q)(1 + cosq) - 3
= cosq( 1 + cosq) - 3
= cosq + cos^2 q - 3
= cosq + 1 - cosq - 3
= -2