Question

if tana=b/a, prove that acos2a+bsin2a=a

Answer 1

Answer on Question #63972 – Math – Trigonometry

Question

If $\tan a = b / a$, prove that $a \cos 2a + b \sin 2a = a$.

Proof

It follows from $\tan a = b / a$ that $\cos a = \frac{a}{b} \sin a$.

Substituting the previous formula into

$$\begin{array}{l} a \cos 2 a + b \sin 2 a = a \left(\cos^ {2} a - \sin^ {2} a\right) + b \cdot 2 \sin a \cos a = \\ = a \left(\cos^ {2} a - \sin^ {2} a\right) + b \cdot 2 \sin a \cdot \frac {a}{b} \sin a = a \left(\cos^ {2} a - \sin^ {2} a\right) + 2 a \sin^ {2} a = \\ = a \left(\cos^ {2} a + \sin^ {2} a\right) = a \end{array}$$

QED

Answer provided by www.AssignmentExpert.com