Question
If tan θ = 4/3 and θ is an acute angle, find the value
of sin θ + cos θ.Solution
Given tan θ = 4/3, From the definition of tan θ, tan θ = opposite/adjacent = 4/3. Using the Pythagorean theorem, Hypotenuse = √(4² + 3²) = √(16 + 9) = √25 = 5. So, sin θ = opposite/hypotenuse = 4/5 and cos θ = adjacent/hypotenuse = 3/5. Now, sin θ + cos θ = 4/5 + 3/5 = 7/5.
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