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θ is an acute angle such that tan(θ) = 12. What is the value of 5√5⋅(sinθ+cosθ)?

1 answer

if tanθ = 12,
sinθ = 12/√145
cosθ = 1/√145
so
5√5⋅(sinθ+cosθ) = 5√5⋅13/√145 = 65/√29
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