Prove cotx=sinxsin(\frac{\pi}{2}-x)+cos^{ 2}xcotx [/tex]

We have to prove that :

For this, let us take the Right Hand Side (RHS) and then prove the Left Hand Side (LHS).

RHS=

= ()

= ()

=

Now, we know that is common in the numerator and thus,

= ()

==LHS

Hence, LHS=RHS and thus the required equation has been proved.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0