Question

If sin theta = 3/5, then cos theta + cot theta is

Answer 1

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Answer 2

Given,

Sin θ = 3 / 5

To Find,

cos θ+ cot θ =?

Solution,

We know from the sin θ formula that,

sin θ = P(Perpendicular)  / H(Hypotenuse) = 3 / 5

Therefore, Perpendicular = 3

Hypotenuse = 5

By Pythagoras theorem,

$P^2 + B^2 = H^2\\3^2 + B^2 = 5^2\\B^2 = 25 - 9 \\B^2 = 16 \\B = \sqrt{16} \\B = 4$

Base = 4

Therefore, Cos θ = B(Base) / H(Hypotenuse)

Cos θ = 4 / 5

Similarly, cot θ = B(Base)  / P(Perpendicular)

cot θ = 4 / 3

Therefore,  cos θ + cot θ = 4 / 5 + 4 / 3

cos θ + cot θ = (12 + 20)/15

cos θ + cot θ = 32 / 15

Hence, If sin theta = 3/5, then cos theta + cot theta is 32 /15