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Question
If 35 sec θ = 37, find the value of sin θ - sin θ tan θ.
Solution
Consider ΔABC, where ∠B = 90°
⇒ 35secθ = 37
⇒ secθ = `(37)/(35)`
⇒ secθ = `"Hypotenuse"/"Base" = "AC"/"BC" = (37)/(35)`
By Pythagoras theorem,
AB2
= AC2 - BC2
= 372 - 352
= (37 + 35)(37 - 35)
= 72 x 2
= 144
⇒ AB = 12
Now,
sinθ = `"Perpendicular"/"Hypotenuse" = "AB"/"AC" = (12)/(37)`
tanθ = `"Perpendicular"/"Hypotenuse" = "AB"/"BC" = (12)/(35)`
∴ sinθ - sinθ tanθ
= `(12)/(37) - (12)/(37) xx (12)/(35)`
= `(12)/(37)(1 - 12/35)`
= `(12)/(37)((35 - 12)/35)`
= `(12)/(37) xx (23)/(35)`
= `(276)/(1295)`.
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