Is cos(pi/3+x)=sin(30-x) ?

The answer to whether cos(pi/3+x)=sin(30-x) is True

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prove cos(pi/3+x)=sin(30-x)

prove

cos (\frac{π}{3} + x) = sin (3 0^{\circ} - x)

True

Solution steps

cos (6 0^{\circ} + x) = sin (3 0^{\circ} - x)

Manipulating left side

cos (6 0^{\circ} + x)

Rewrite using trig identities

= \frac{1}{2} cos (x) - \frac{3}{2} sin (x)

Manipulating right side

sin (3 0^{\circ} - x)

Rewrite using trig identities

= \frac{1}{2} cos (x) - \frac{3}{2} sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x) - tan (\frac{π}{18}) = 1 + tan (x) tan (\frac{π}{18})

cos (θ) = \frac{2}{5}, cot (θ) < 0

θ, cos (θ) = \frac{2}{2}

b, s (t) = tan (b t^{2})