Question

addition and subtraction formulae of trigonometry ​

Answer 1

Answer:

Formulae are as follows:

Sine of sum of angles:

\sin (A+B) = \sin A . \cos B + \cos A . \sin B

Cosine of sum of angles:

\cos (A+B) = \cos A . \cos B - \sin A . \sin B

Sine of difference of angles:

\sin (A-B) = \sin A . \cos B - \cos A . \sin B

Cosine of difference of angles:

\cos (A-B) = \cos A . \cos B + \sin A . \sin B

And similarly the sum and difference of angle formula of Tangent are:

\tan (A+B) = \dfrac{\tan A + \tan B}{1 - \tan A . \tan B}

and,

\tan (A-B) = \dfrac{\tan A - \tan B}{1 + \tan A . \tan B}

Answer 2

Answer:

sinα = a/c, cosα = b/c.

sin(90° - α) = cosα and cos(90° - α) = sinα,

sin(α + β) = sinα cos β + cos α sin β.

cos(α + β) = cosα cos β - sin α sin β.

sin(α - β) = sinα cos β - cos α sin β.

cos(α - β) = cosα cos β + sin α sin β