If tan θ=1 and θ is acute find the value of sin θ+cosθ
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Step-by-Step Solution
Step 1: Determine the angle θ
We are given that tanθ=1 and θ is an acute angle. We know that the tangent of 45∘ is 1. Therefore, the angle θ must be 45∘.
Step 2: Find the values of sinθ and cosθ
Now that we know θ=45∘, we can find the values of sin45∘ and cos45∘. Both sin45∘ and cos45∘ are equal to 21.
Step 3: Calculate sinθ+cosθ
Finally, we substitute the values of sin45∘ and cos45∘ into the expression sinθ+cosθ. We add the two fractions and then rationalize the denominator to simplify the expression.