If tan(A/2)=1/3, then the value of tanA+sinA is equal to
We can use the half-angle formula for tangent to solve this. The formula states that tan(A/2) = (1 - cosA) / sinA. Given that tan(A/2) = 1/3, we can substitute it into the formula:
1/3 = (1 - cosA) / sinA
Solving for cosA gives: cosA = 2/3
Using the Pythagorean identity for sinA: sin^2(A) + cos^2(A) = 1, we can find sinA:
sin^2(A) + (2/3)^2 = 1
sin^2(A) = 5/9
sinA = √(5/9) = √5/3
Now we can find tanA:
tanA = sinA / cosA = (√5/3) / (2/3) = √5 / 2
Finally, to find tanA + sinA:
tanA + sinA = √5 / 2 + √5/3
Combining the fractions, we get: (3√5 + 2√5) / 6 = (5√5) / 6.
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If tan(A/2)=1/3, then the value of tanA+sinA is equal to
We can use the half-angle formula for tangent to solve this. The formula states that tan(A/2) = (1 - cosA) / sinA. Given that tan(A/2) = 1/3, we can substitute it into the formula:
1/3 = (1 - cosA) / sinA
Solving for cosA gives: cosA = 2/3
Using the Pythagorean identity for sinA: sin^2(A) + cos^2(A) = 1, we can find sinA:
sin^2(A) + (2/3)^2 = 1
sin^2(A) = 5/9
sinA = √(5/9) = √5/3
Now we can find tanA:
tanA = sinA / cosA = (√5/3) / (2/3) = √5 / 2
Finally, to find tanA + sinA:
tanA + sinA = √5 / 2 + √5/3
Combining the fractions, we get: (3√5 + 2√5) / 6 = (5√5) / 6.