Where is this double angle from (2Cos²X-1)

Question

ScanSolve AI Tutor · Accepted Answer

The double angle identity cos 2x = 2cos² x − 1 is derived from the cosine addition formula and the Pythagorean identity. Step 1: Start with the cosine addition formula. cos(A+B) = cos A cos B − sin A sin B; Step 2: Let A=x and B=x. cos(x+x) = cos x cos x − sin x sin x; cos 2x = cos² x − sin² x; Step 3: Use the Pythagorean identity sin² x + cos² x = 1, which means sin² x = 1 − cos² x. Substitute this into the equation from Step 2: cos 2x = cos² x − (1 − cos² x) Step 4: Simplify the expression. cos 2x = cos² x − 1 + cos² x; cos 2x = 2cos² x − 1; This shows how the identity cos 2x = 2cos² x − 1 is derived.

Where is this double angle from (2Cos²X-1)

Answer

Step-by-step solution

Start with the cosine addition formula.

Let $A=x$ and $B=x$ .

Use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$ , which means $\sin^2 x = 1 - \cos^2 x$ .

Simplify the expression.

Still stuck on this one?

More Mathematics Questions

Where is this double angle from (2Cos²X-1)

Answer

Step-by-step solution

Start with the cosine addition formula.

Let A=xA=xA=x and B=xB=xB=x.

Use the Pythagorean identity sin⁡2x+cos⁡2x=1\sin^2 x + \cos^2 x = 1sin2x+cos2x=1, which means sin⁡2x=1−cos⁡2x\sin^2 x = 1 - \cos^2 xsin2x=1−cos2x.

Simplify the expression.

Still stuck on this one?

More Mathematics Questions

Let $A=x$ and $B=x$ .

Use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$ , which means $\sin^2 x = 1 - \cos^2 x$ .