SOLUTION: cos(2tan^-1(2/1))

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Question 1169459: cos(2tan^-1(2/1))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%282tan%5E-1%282%2F1%29%29
Use the following identity :
cos%282x%29=+%28-1%2B2+cos+%5E2%28x%29%29
since x=tan%5E-1%282%2F1%29=tan%5E-1%282%29, we have
cos%282tan%5E-1%282%29%29=+%28-1%2B2cos+%5E2%28tan%5E-1%282%29%29%29
Use the following identity: cos%28tan%5E-1%28x%29%29=%28sqrt%281%2Bx%5E2%29%2F%281%2Bx%5E2%29%29
cos%282tan%5E-1%282%2F1%29%29=+%28-1%2B2%28sqrt%281%2Bx%5E2%29%2F%281%2Bx%5E2%29%29%5E2%29
cos%282tan%5E-1%282%2F1%29%29=+%28-1%2B2%28sqrt%281%2B2%5E2%29%2F%281%2B2%5E2%29%29%5E2%29
cos%282tan%5E-1%282%2F1%29%29=+-1%2B2%28%281%2B4%29%2F%281%2B4%29%5E2%29

cos%282tan%5E-1%282%2F1%29%29=+-1%2B2%285%2F25%29

cos%282tan%5E-1%282%2F1%29%29=+-1%2B2%2F5+
cos%282tan%5E-1%282%2F1%29%29=+-3%2F5+
cos%282tan%5E-1%282%2F1%29%29=+-0.6+