To simplify the expression 2cos²(x/2) - 12, we can break it down step by step:
Use the double angle identity for cosine: cos(2θ) = 2cos²(θ) - 1Substitute x/2 for θ: cos(x) = 2cos²(x/2) - 1Bring the 1 to the other side: 2cos²(x/2) = cos(x) + 1Divide both sides by 2: cos²(x/2) = 0.5cos(x) + 0.5Multiply by 2 to get rid of the 2 in the denominator and simplify: cos²(x/2) = cos(x) + 1
Therefore, the simplified expression is cos(x) + 1 - 12.
To simplify the expression 2cos²(x/2) - 12, we can break it down step by step:
Use the double angle identity for cosine: cos(2θ) = 2cos²(θ) - 1Substitute x/2 for θ: cos(x) = 2cos²(x/2) - 1Bring the 1 to the other side: 2cos²(x/2) = cos(x) + 1Divide both sides by 2: cos²(x/2) = 0.5cos(x) + 0.5Multiply by 2 to get rid of the 2 in the denominator and simplify: cos²(x/2) = cos(x) + 1Therefore, the simplified expression is cos(x) + 1 - 12.