Question

find answer of this​

Answer 1

Answer:

$\sqrt{a^{2} + b^{2} - c^{2} }$

Step-by-step explanation:

$a \cos( \alpha ) - b \sin( \alpha ) = c \: \: \: \: \: ....(1)$

Let,

$a \sin( \alpha ) + b \cos( \alpha ) = x \: \: \: \: \: \: \: \:...(2)$

Divide both sides of the equation 1 and 2 by

$\sqrt{a^{2} + b^{2} }$

Now let

$\frac{a}{ \sqrt{a^{2} + b^{2} } } = \cos( \beta )$

So the equation 1 becomes

$\cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) = \frac{c}{ \sqrt{a^{2} + b^{2} } }$

$\cos( \alpha + \beta ) = \frac{c}{ \sqrt{a^{2} + b^{2} } }$

$\sin( \alpha + \beta ) = \sqrt{ \frac{a^{2} + b^{2} -c^{2} }{a^{2} + b^{2} } }$

Also Equation 2 becomes

$x = \sin( \alpha + \beta ) \times \sqrt{a^{2} + b^{2} }$

therefore

$x = \sqrt{a^{2} + b^{2} - c^{2} }$