Question

Verify that the equation is an identity. (Hint: \cos2x=\cos(x+x).) \cos2x+2\sin^{2}x-1=0

Trigonometric equation and identitie
ANSWERED
asked 2021-06-05
Verify that the equation is an identity. (Hint: \(\cos2x=\cos(x+x)\).)
\(\cos2x+2\sin^{2}x-1=0\)

Answers (1)

2021-06-06

Step 1
\(\cos(2x)=\cos(x+x)\)
\(=\cos(x)\cos(x)-\sin(x)\sin(x)\)
Since \(\cos(A+B)=\cos A\cos B-\sin A\sin B\)]
\(=cos^{2}(x)-\sin^{2}(x)\)
\(\cos(2x)+2\sin^{2}(x)-1=\cos^{2}(x)-\sin^{2}(x)+2\sin^{2}(x)-1\)
\(=\cos^{2}(x)+\sin^{2}(x)-1\)
\(=1-1\)
\(=0\)

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