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Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
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Solution
We know that `cos theta = "adjacent side"/"hypotenuse"`
Let us consider a right-angled ΔABC
Let opposite side BC = x.
By applying Pythagoras theorem, we get
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
25 = x + 16
x = 25 - 16 = 9
x = `sqrt9 = 3`
We know that `cosA = 4/5`
`sin A = "opposite side"/"hypotenuse" = 3/5`
`tan A = "opposite side"/"adjacent side" = 3/4`
`cosec A = 1/(sin A) = (1/3)/5 = 5/3`
`sec A = 1/(cos A) = (1/4)/5 = 5/4`
`cot A = 1/(tan A) =(1/3)/4 = 4/3`
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