Is cos(2*x)=2*cos^2(x)-1 ?

The answer to whether cos(2*x)=2*cos^2(x)-1 is True

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prove cos(2x)=2cos^2(x)-1

prove

cos (2 \cdot x) = 2 \cdot cos^{2} (x) - 1

True

Solution steps

cos (2 x) = 2 cos^{2} (x) - 1

Manipulating left side

cos (2 x)

Rewrite using trig identities

= cos^{2} (x) - sin^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= cos^{2} (x) - (1 - cos^{2} (x))

Simplify

cos^{2} (x) - (1 - cos^{2} (x)) : 2 cos^{2} (x) - 1

= 2 cos^{2} (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

csc (x) tan (x) + sec (x) = 2 sec (x)

csc (x) (sin (x) + tan (x)) = 1 + sec (x)

\frac{1}{tan ( 7 0 ^{\circ} )} = cot (7 0^{\circ})

\frac{sec ( A )}{sin ( A )} - \frac{sin ( A )}{cos ( A )} = cot (A)

csc (θ) = sec (θ) cot (θ)