Is sin(pi/6+x)=cos(pi/3-x) ?

The answer to whether sin(pi/6+x)=cos(pi/3-x) is True

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prove sin(pi/6+x)=cos(pi/3-x)

prove

sin (\frac{π}{6} + x) = cos (\frac{π}{3} - x)

True

Solution steps

sin (\frac{π}{6} + x) = cos (\frac{π}{3} - x)

Manipulating left side

sin (\frac{π}{6} + x)

Rewrite using trig identities

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

Manipulating right side

cos (\frac{π}{3} - 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) - 1 = 0

(1 + cos (2 θ)) (1 - cos (2 θ)) = sin^{2} (2 θ)

sin (x) - cos (x) = 0

sin (2 θ) + cos (2 θ) = 2 sin (θ) cos (θ) + 2 cos^{2} (θ) - 1

\frac{tan ^{4} ( x ) - 1}{tan ^{2} ( x ) - 1} = sec^{2} (x)

Is sin(pi/6+x)=cos(pi/3-x) ?
The answer to whether sin(pi/6+x)=cos(pi/3-x) is True