Is cos(x-y)=cos(y-x) ?

The answer to whether cos(x-y)=cos(y-x) is True

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prove cos(x-y)=cos(y-x)

prove

cos (x - y) = cos (y - x)

True

Solution steps

cos (x - y) = cos (y - x)

Manipulating left side

cos (x - y)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (- x + y)

= cos (y - x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ^{2} ( x )}{csc ^{2} ( x )} = tan^{2} (x)

tan (A + B) + tan (A - B) = \frac{( 2 sin ( 2 A ) )}{( cos ( 2 A ) + cos ( 2 B ) )}

cos (3 θ) = 4 cos^{3} (θ) - cos (θ)

\frac{1 + csc ( b )}{cot ( b ) + cos ( b )} = sec (b)

\frac{1 + tan ^{2} ( θ )}{tan ( θ )} = sec (θ) csc (θ)