Is sin^2(pi/2-x)+sin^2(x)=1 ?

The answer to whether sin^2(pi/2-x)+sin^2(x)=1 is True

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prove sin^2(pi/2-x)+sin^2(x)=1

prove

sin^{2} (\frac{π}{2} - x) + sin^{2} (x) = 1

True

Solution steps

sin^{2} (\frac{π}{2} - x) + sin^{2} (x) = 1

Manipulating left side

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

Rewrite using trig identities

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

Remove parentheses:

(a) = a

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos (x) - csc (x) cot (x) = - cos (x) cot^{2} (x)

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

\frac{1 + tan ( x )}{sin ( x )} - sec (x) = csc (x)

\frac{csc ( β )}{cot ( β )} = sec (β)

\frac{cot ( θ ) - csc ( θ )}{cot ( θ ) + csc ( θ )} = \frac{1 - 2 cos ( θ ) + cos ^{2} ( θ )}{- sin ^{2} ( θ )}

Is sin^2(pi/2-x)+sin^2(x)=1 ?
The answer to whether sin^2(pi/2-x)+sin^2(x)=1 is True