Question

If $8$ $cosx+15sinx=15$ and $cosx\ne 0$, then $8$ $sinx-15cosx=$

• A. 8
• B. -8
• C. 15
• D. -15

Answer 1

The correct option is A 8

$8$ $cosx+15\sin x=15$ ........ (1)

and $cosx\ne 0$, then $8$ $sinx-15\cos x=?$

squaring and adding both the equations, we get,

$(8\cos x+15\sin x{)}^2+(8\sin x-15\cos x{)}^2$

$64({\cos }^{2}x+{\sin }^{2}x)+225({\cos }^{2}x+{\sin }^{2}x)=289$

$(8\sin x-15\cos x{)}^2=289-{15}^2=64$

$\therefore 8\sin x-15\cos x=\pm 8$

$\therefore 8\sin x-15\cos x=8$ ........ (2)

$\therefore 8\sin x-15\cos x=-8$ ...........(3)

Adding (1) and (2)

$\therefore 23\sin x-7\cos x=23$ This relation is possible only if $\cos x=0$ but given condition is $\cos x\ne 0$

So relation (2) is rejected and relation (3) is accepted.

This means option A is correct.