show that √3 cosec 20°- sec 20° = 4​

Question

show that √3 cosec 20°-
sec 20° = 4​

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Sadie 2 months 2021-08-13T13:20:06+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-13T13:21:10+00:00

    Answer:

    have a nice day

    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

    0
    2021-08-13T13:21:59+00:00

    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

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