#6 in image Double and Half AnglesLet's start with the formula for the cosine of a sum:cos(A + B) = cos(A) cos(B) – sin(A) sin(B)Now replace B with A and simplify and we get a double angle formula:(1)cos(2A) = (cos(A))² – (sin(A))²(2)Now do the same with sine:sin(A + B) = sin(A) cos(B) + cos(A) sin(B)(3)So,sin(2A) = 2 sin(A) cos(B)(4)To get half angle formulas we start with (2) above and replace (sin(A))² with1- (cos(A))? to getcos(2A) = 2(cos(A))² –When we solve this equation for cos(A), we get|1+cos(2A)cos(A) =Finally, replace A with - to get the half angle formula:|1+cos(0)Cos= +(5)2In this formula, you have consider the quadrant of - to decide if you should keep theplus or minus sign.See if you can start with (2) above and derive the other half angle formula:|1-cos(0)sinNow see if you can use your higher order thinking skills to prove the followingidentities:1. sin(3x) = (sin(x))(4(cos(x))² – 1)2. cos(4x) = 1– 8(sin(x))²(cos(x))²3. sin(3x) = (sin(x))(3 – 4(sin(x))²)4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1)Finally, find the following without a calculator:5. tan6. cos()

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(6)Given the trigonometric ratiocos(7π8)

6. cos( 8.