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Question
If 2 cos θ = `sqrt(3)`, then find all the trigonometric ratios of angle θ
Solution
2 cos θ = `sqrt(3)`
⇒ cos θ = `sqrt(3)/2`
AB2 = AC2 – BC2
= `2^2 - (sqrt(3))^2`
⇒ 4 – 3 = 1
AB = `sqrt(1)` = 1
sin θ = `"opposite side"/"hypotenuse" = 1/2`
cos θ = `"adjacent side"/"hypotenuse" = sqrt(3)/2`
tan θ = `"opposite side"/"adjacent side" = 1/sqrt(3)`
cosec θ = `"hypotenuse"/"opposite side"` = 2
sec θ = `"hypotenuse"/"adjacent side" = 2/sqrt(3)`
cot θ = `"adjacent side"/"opposite side" = sqrt(3)`
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