Derive these identities using the addition or subtraction formulas for sine or cosine:

a. sin a sin b = 1 / 2(cos(a – b) – cos(a + b))

b. sin a cos b = 1 / 2(sin(a + b) + sin(a – b))

Step-by-step explanation:

cos(a-b)-cos(a+b)=2(sina x sinb)

using formulae of cos (a-b) & cos(a+b)

cos a cos b + sina sinb - cosa cosb + sina sinb=2 sina sinb

2 sina sinb = 2 sina sinb

proved!

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: