Question

(sinx-1)(sinx+cos^2x) multiply and simplify

Answer 1

$\bf [sin(x)-1][sin(x)+cos^2(x)]\\\\ -------------------------------\\\\ sin^2(x)+sin(x)cos^2(x)-sin(x)-cos^2(x) \\\\\\\ [sin^2(x)-cos^2(x)]+[sin(x)cos^2(x)-sin(x)] \\\\\\ -[cos^2(x)-sin^2(x)]-[sin(x)-sin(x)cos^2(x)] \\\\\\ -[\stackrel{cos(2x)}{cos^2(x)-sin^2(x)}]-sin(x)\stackrel{sin^2(x)}{[1-cos^2(x)]} \\\\\\ -cos(2x)-sin(x)sin^2(x)\implies -cos(2x)-sin^3(x)$