SOLUTION: 1.Derive a formula for cos 2A with aid of cos (A + B). 2.Prove that 2 tan x + 2 cot x = 4/sin 2x

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1.Derive a formula for cos 2A with aid of cos (A + B). 2.Prove that 2 tan x + 2 cot x = 4/sin 2x      Log On


   

Question 605241: 1.Derive a formula for cos 2A with aid of cos (A + B).
2.Prove that 2 tan x + 2 cot x = 4/sin 2x
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1.Derive a formula for cos 2A with aid of
cos (A + B).
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

Substitute A for B

cos(A + A) = cos(A)cos(A) - sin(A)sin(A)

Simplifying,

cos(2A) = cosē(A) - sinē(A)

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2.Prove that
2·tan(x) + 2·cot(x) = 4%2Fsin%282x%29
2·sin%28x%29%2Fcos%28x%29 + 2·cos%28x%29%2Fsin%28x%29

2sin%28x%29%2Fcos%28x%29 + 2cos%28x%29%2Fsin%28x%29

Get LCD of sin(x)cos(x)

%282sin%5E2%28x%29+%2B+2cos%5E2%28x%29%29%2F%28sin%28x%29cos%28x%29%29

%282%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29%29%2F%28sin%28x%29cos%28x%29%29

%282%281%29%29%2F%28sin%28x%29cos%28x%29%29

+2%2F%28+sin%28x%29cos%28x%29+%29+

Multiply by 2%2F2

4%2F%282sin%28x%29cos%28x%29%29

4%2Fsin%282x%29

Edwin