Question

if 3 sin theta + 5 cos theta = 5 then 5 sin theta - 3 cos theta =?
pls help me na

Answer 1

Answer:

Let 5 sin x - 3 cos x = k

then

$(3sin \: x + 5cos \: x) {}^{2} + (5sin \: x \: - 3cos \: x) {}^{2} = {5}^{2} + {k}^{2}$

$9 + 25 = 25 + {k}^{2}$

${k}^{2} = 9$

$k = 3$