Question

Question #efceb

Answer 1

Start from the left-hand side:
`sin^2(x)cos^4(x)`
`=(1-cos^2(x))cos^4(x)` {since `sin^2(x)+cos^2(x)=1`}
`=cos^4(x)-cos^6(x)`

Compare it to the right-hand:
`cos^2(x)+cos^4(x)-cos^6(x)`

Thus, the equation in the question only holds when `cos^2(x)=0`, or `x=(2k+1)pi,kinZZ`. Any value outside this range invalidates the equation.

This can be verified by a graph of the two sides of the equation:
graph{(y-(sin(x))^2 (cos(x))^4)(y-(cos(x))^2-(cos(x))^4+(cos(x))^6)=0 [-10, 10, -0.25, 1.25]}

As seen, they only intersect when `x=(2k+1)pi,kinZZ`.