Chapter 7, Problem 4RCC

(a)

To determine

To state: Addition Formulas for Sine, Cosine and Tangent.

Answer to Problem 4RCC

The Addition Formulas for sine, cosine and Tangent are explained below.

Explanation of Solution

Given information:

The trigonometry functions are sine, cosine and tangent.

Calculation:

The addition formula for sine is as follows.

  $\sin \left(s+t\right)=\sin s\cos t+\cos s\sin t$

The addition formula for cosine is as follows.

  $\cos \left(s+t\right)=\cos s\cos t-\sin s\sin t$

The addition formula for tangent is as follows.

  $\tan \left(s+t\right)=\frac{\tan s+\tan t}{1-\tan s\tan t}$

(b)

To determine

To state: Subtraction Formulas for Sine, Cosine and Tangent.

Answer to Problem 4RCC

The Subtraction Formulas are explained below.

Explanation of Solution

Given information:

The trigonometry functions are sine, cosine and tangent.

Calculation:

The subtraction formula for sine is as follows.

  $\sin \left(s-t\right)=\sin s\cos t-\cos s\sin t$

The addition formula for cosine is as follows.

  $\cos \left(s-t\right)=\cos s\cos t+\sin s\sin t$

The addition formula for tangent is as follows.

  $\tan \left(s-t\right)=\frac{\tan s-\tan t}{1+\tan s\tan t}$