Question

If 3 costheta+ 4 sintheta=Asin(theta+ a), then values of Aand
a are​

Answer 1

Answer:

A= 5 &

$a = {tan}^{ - 1} \frac{4}{3}$

Explanation:

$Given \: it \: \\ = 3cos \alpha + 4sin \alpha = Asin( \alpha +a) .....(1)\\ multiplying \: and \: divide \: by \: \sqrt{ {3}^{2} + {4}^{2} } = 5 \\ = 5( \frac{3}{5} cos \alpha + \frac{4}{5 } sin \alpha ) \\ = 5(sin \alpha cos a + cos \alpha sin a ) \: \: \\ where \: sin a = \frac{3}{5} \: \: \: \: \: \: \: \: cos a = \frac{4}{5 } \\ = 5sin( \alpha + a ) \\ where \: a = {tan}^{ - 1} ( \frac{3}{4} ) \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: A =5$

Hope it will help you...