Question
If 5tanθ = 12, then find the value of (sinθ – cosθ).
Solution
We have, 5tanθ = 12
So, tan θ = (12/5)
Or, (perpendicular/base) = (12/5)
So, hypotenuse 2 = base 2 + perpendicular 2 = 5 2 + 12 2
So, hypotenuse = √169 = 13
So, sin θ = (perpendicular/hypotenuse) = (12/13)
And, cos θ = (base/ hypotenuse) = (5/13)
Therefore, sin θ – cos θ = (12/13) – (5/13) = (7/13)
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