Question

If $5\cos \theta +12\sin \theta =13,$ then $\sin \theta$ is

• A. $\frac{5}{12}$
• B. $\frac{1}{13}$
• C. $\frac{12}{13}$
• D. None of the above

Answer 1

The correct option is C $\frac{12}{13}$

If $a\sin \theta +b\cos \theta =c$ then
$a\cos \theta -b\sin \theta =\sqrt{(a^2+b^2-c^2)}$ (Eq1) (PROPERTY)
As per question
$a=12$
$b=5$
$c=13$
$5\cos \theta +12\sin \theta =13$ (Eq2)
By putting the values in Eq 1 we get $12\cos \theta -5\sin \theta =0$ (Eq3)
On solving both Eq 2 and Eq 3 we get $\sin \theta =\frac{12}{13}$