Question

DETAILS MCKTRIG8 5.3.051. (-/1 Points] Prove the following identity. sin 30 -3 sine 4 sino We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30 = sin + sin cos 8) + (con 20)(sin) - (2 sin e. (cos 8) + (1 - 2 sin )(win ) - 2 sin sin 0 - 2 sino - (2 sin 0(1- + sin - 2 sino - 2 sino- + sin - 2 sine D-3 sin 8-4 sino Need Help? Read it Talk to a Tutor

Answer 1

sin (30) = 3 sino - 4 sin3 o 1.H.S. sin (30) U o) sin(120 to = (sin2@) (case) + (60820). (sino) - (2 sino caso). Cos 0) + (1 - 251529) (sino) 2 sino cos²o + sino a sino (2 sino) (1 - sino) + sino - 2 singo - 2 sino 12 sin3o + sino a sin3o IT 3 sine 4 sino R.H.S. Sin 4A - 4 sin A COBA 4 sin3A COSA L.H.S. sin 4A 2 (sin 2A) ( cos 24 24) - alasinA.COSA cos²A sin? A 4 sin A. Cos²A 4 sin3A . COSA R.H.S.