Prove that: (sin x - 2 sin³ x)/(2 cos³ x - cos x) = tan x

We have to prove that:

Taking LHS, we get:

We can take sin(x) as common from numerator part. We get:

Similarly, we can take cos(x) as common from first two terms. We get:

As we know that:

We get:

Now, we will expand the terms in fraction:

As we know that:

Now substitute the values in the expression, we get:

Here, we notice that LHS = RHS

Proved.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

8(-10x+3.5y-7)

8×-10x + 8×3.5y + 8×-7

-80x + 28y - 56

therefore

-80x+28y-56 is the correct answer