√3 cosec 20° - sec 20° =

Question

√3 cosec 20° - sec 20° = (A) 4 (B) 2 (C) 1 (D) 3

Tardigrade Admin · Accepted Answer

√3 cos e 20°-sec 20° =(√3/sin 20° )-(1/cos 20°) =(√3cos 20°-sin 20°/sin 20°. cos 20°) =(2[(√3/2) cos 20°-(1/2) sin 20°]/(1)2[2 sin 20°. cos 20°]) = 4([sin 60°. cos 20°-cos 60°. sin 20°]/sin 40°) =4(sin(60°-20°)/sin 40°) =4(sin 40°/sin 40°) =4

Q. 3​cosec20∘−sec20∘ =

4

2

1

3

3​cose20∘−sec20∘ =sin20∘3​​−cos20∘1​ =sin20∘.cos20∘3​cos20∘−sin20∘​ =21​[2sin20∘.cos20∘]2[23​​cos20∘−21​sin20∘]​ =4sin40∘[sin60∘.cos20∘−cos60∘.sin20∘]​ =4sin40∘sin(60∘−20∘)​ =4sin40∘sin40∘​ =4

Q. $3 cosec 2 0^{\circ} - sec 2 0^{\circ}$ =