Question

If $3sinA+5cosA=5,$ then value of $(3cosA-5sinA{)}^2$ is-

• A. $4$
• B. $9$
• C. $5$
• D. $2$

Answer 1

The correct option is B $9$

$3\sin A+5\cos A=5$

$\Rightarrow (3\sin A+5\cos A{)}^2=25$

$\Rightarrow 9{\sin }^{2}A+25{\cos }^{2}A+30\sin A\cos A=25$ ……$\left(1\right)$

Let $(3\cos A-5\sin A{)}^2=k$

$\Rightarrow 9{\cos }^{2}A+25{\sin }^{2}A-30\sin A\cos A=k$ …….$\left(2\right)$

$\left(1\right)+\left(2\right)$

$\Rightarrow 9({\sin }^{2}A+{\cos }^{2}A)+25({\cos }^{2}A+{\sin }^{2}A)=25+k$

$\Rightarrow 9+25=25+k$

$\Rightarrow k=9$.