Is sin(pi/2-x)=sin(pi/2+x) ?

The answer to whether sin(pi/2-x)=sin(pi/2+x) is True

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prove sin(pi/2-x)=sin(pi/2+x)

prove

sin (\frac{π}{2} - x) = sin (\frac{π}{2} + x)

True

Solution steps

sin (\frac{π}{2} - x) = sin (\frac{π}{2} + x)

Manipulating right side

sin (\frac{π}{2} + x)

Rewrite using trig identities

= cos (x)

Use the following identity:

cos (x) = sin (\frac{π}{2} - x)

= sin (\frac{π}{2} - x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ^{2} ( t )}{cos ( t )} = sec (t) - cos (t)

tan (θ) + cot (θ) = 2 csc (2 θ)

csc^{4} (x) - cot^{4} (x) = 2 cot^{2} (x) + 1

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

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

Is sin(pi/2-x)=sin(pi/2+x) ?
The answer to whether sin(pi/2-x)=sin(pi/2+x) is True