Question

here is my question
please answer it

Answer 1

Hola there...

Given:

$a \cos\alpha + b \sin\alpha = m$

and

$a \sin\alpha - b \cos\alpha = n$

We will square both the equation and then we will get the equation as follows:

${ {a}^{2} \cos\ }^{2} \alpha + {b}^{2} { \sin}^{2} \alpha +2 a \cos \alpha b \sin \alpha ) = {m}^{2}$

and

${a}^{2} { \sin}^{2} \alpha + {b}^{2} { \cos }^{2} \alpha - 2a \sin\alpha b \cos\alpha$

Now, we will add both the equation that we have got after squaring

${a}^{2} {cos}^{2} \alpha + {a}^{2} {sin}^{2} \alpha + {b}^{2} {sin}^{2} \alpha + {b}^{2} {cos \alpha }^{2} + 2abcos \alpha sin \alpha - 2abcos \alpha sin \alpha = {m}^{2} + {n}^{2}$

as we know that sin² + cos² = 1

So, now we will get the following results:

${a}^{2} + {b}^{2} = {m}^{2} + {n}^{2}$

So, option (d) m² + n² is the correct answer.

Hope this helps...:)