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Question
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
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Solution
We know that `cos theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"`
Let us consider right angled Δle ABC
Let x be the opposite side, By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
25 = 𝑥2 + 9
𝑥2 = 16 ⇒ 𝑥 = 4
`sin theta = (AB)/(AC) = 4/5`
`tan theta = (AB)/(BC) = 4/3`
Substitute sin 𝜃, tan 𝜃 in the equation we get
`(sin theta 1/(tan theta))/(2 tan theta) = (4/5 - 3/4)/(2 xx 4/3)`
`= ((16 - 15)/20)/(8/3)`
= `(1/20)/(8/3)`
`= 1/20 xx 8/3 = 3/160`
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