Question

If sin theta =3/5 evaluate 3sin theta+5cos theta/3sin theta-5cos theta

Answer 1

Given, 3 sinθ+ 5 cosθ= 5(3 sinθ +5 cosθ)2+ (5 sinθ– 3 cosθ)2= 9 sin2θ+ 25 cos2θ+ 30 sinθcosθ+ 25 sin2θ+ 9 cos2θ–30 sinθcosθ= 34 sin2θ+ 34 cos2θ= 34 (sin2θ+ cos2θ)= 34 (sin2θ+ cos2θ= 1)∴ (5)2+(5 sinθ– 3 cosθ)2= 34 ⇒25 + (5 sinθ– 3 cosθ)2= 34⇒ (5 sinθ–3 cosθ)2= 34 – 25⇒ (5 sinθ–3 cosθ)2= 9⇒5 sinθ– 3 cosθ= ± 3