Question

show that √3 cosec 20°-
sec 20° = 4​

Answer 1

Answer:

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Step-by-step explanation:

Given expression is sin20∘3−cos20∘1

=2(sin20∘3/2−cos20∘1/2)

=2(sin20∘sin60∘−cos20∘cos60∘)

=2(sin20∘cos20∘sin60∘cos20∘−cos60∘sin20∘)

=2(sin20∘cos20∘sin(60∘−20∘))

=2sin20∘cos20∘sin40

Answer 2

Step-by-step explanation:

Question :

Show that √3 cosec 20° - sec 20° = 4

Solution :

Considering L.H.S :

⇒ √3/sin 20° - 1/cos 20° = √3cos20° - sin20°/sin20°cos20°

⇒ 2(√3/2 - cos20° - 1/2sin20°)/sin20°cos20°

⇒ 2(sin60°cos20° - cos60°sin20°)/sin20°cos20°

⇒ 2sin(60° - 20°)/sin20°cos20°

⇒ 2sin40°/sin20°cos20°

⇒ 4sin40°/2sin20°cos20°

⇒ 4sin40°/sin40° = 4