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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Use the negative angle identity:

sin (- x) = - sin (x)

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

Use the negative angle identity:

cos (- x) = cos (x)

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

Simplify

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( x ) - cos ( x )}{tan ( x )} = sin (x)

sin (2 x) = 2 cos (x) sin (x)

cos (x + π) = - cos (x)

sin (x) sec (x) cot (x) = 1

tan (2 u) = \frac{2 cot ( u )}{csc ^{2} ( u ) - 2}