Is cos(x+y)-cos(x-y)=-2sin(x)sin(y) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(x+y)-cos(x-y)=-2sin(x)sin(y)

prove

cos (x + y) - cos (x - y) = - 2 sin (x) sin (y)

True

Solution steps

cos (x + y) - cos (x - y) = - 2 sin (x) sin (y)

Manipulating right side

- 2 sin (x) sin (y)

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

sec (\frac{π}{2} - u) = csc (u)

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) (csc^{2} (- 1))

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

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

cot (\frac{1}{x}) = cos (\frac{1}{x}) arcsin (\frac{1}{x})

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