SOLUTION: Show that: sin x cos^2x - sin x = -sin^3x

Algebra ->  Trigonometry-basics -> SOLUTION: Show that: sin x cos^2x - sin x = -sin^3x      Log On


   

Question 906062: Show that: sin x cos^2x - sin x = -sin^3x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28x%29+cos%5E2%28x%29+-+sin+%28x%29+=+-sin%5E3%28x%29+ ....substitute cos%5E2%28x%29 with +1-sin%5E2%28x%29+

+highlight%28sin%28x%29%281-sin%5E2%28x%29%29%29+-+sin+%28x%29+=+-sin%5E3%28x%29+ ...multiply +highlight%28sin%28x%29%281-sin%5E2%28x%29%29%29+

+sin%28x%29%2A1-sin%28x%29%2Asin%5E2%28x%29+-+sin+%28x%29+=+-sin%5E3%28x%29+

+sin%28x%29-sin%5E3%28x%29+-sin+%28x%29+=+-sin%5E3%28x%29+

+cross%28sin%28x%29%29-sin%5E3%28x%29+-cross%28sin+%28x%29%29+=+-sin%5E3%28x%29+

+-sin%5E3%28x%29++=+-sin%5E3%28x%29+