If $3sin\theta + 5cos\theta$ = 5, then $5sin\theta - 3cos\theta$ is equal to
1). $\pm 3$
2). $\pm 5$
3). 1
4). $\pm 2$
3 sin$\theta$ + 5 cos$\theta$ = 5 ...(i)
5 sin$\theta$ – 3 cos$\theta$ = x ...(ii)
On squaring and adding,
9 sin2$\theta$ = + 25 cos2$\theta$ + 25 sin2$\theta$ + 9cos2$\theta$ = 25 + x2
=> 9 (sin2$\theta$ + cos2$\theta$ ) + 25 (cos2$\theta$ +sin2$\theta$ ) = 25 + x2
=> 9 + 25 = 25 + x2
=> x2 = 9
=> x = ±3 .