Question

prove that sin(40+x).cos(10+x)-cos(40+x).sin(10+x)=1/2

Answer 1

Answer on QUESTION #55951 – Math – Trigonometry

Prove that $\sin (40 + x) * \cos (10 + x) - \cos (40 + x) * \sin (10 + x) = \frac{1}{2}$

SOLUTION

First of all we recall a formula of trigonometry:

$$\sin (\alpha) * \cos (\beta) - \cos (\alpha) * \sin (\beta) = \sin (\alpha + \beta)$$

in our case $\alpha = 40 + x$ and $\beta = 10 + x$

Now apply the formula to our case

$$\begin{array}{l} \sin (40 + x) * \cos (10 + x) - \cos (40 + x) * \sin (10 + x) = \sin ((40 + x) - (10 + x)) = \\ = \sin (40 + x - 10 - x) = \sin (30) = \frac{1}{2} \end{array}$$

**REMARK**

The solution is true only in the case where the argument is recorded in degrees. If the argument records in radians, then $\sin(30) = -0.988031$.

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