How do you simplify (sin theta csc theta)/cot theta?

2 Answers
Mar 11, 2018

color(green)(tan theta

Explanation:

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From the above trigonometric identities,

csc theta = (1 / sin theta), cot theta = 1/ tan theta = cos theta / sin theta

Substituting the above in the given sum,

(cancel sin theta * (1/ cancel sin theta) ) / (cos theta / sin theta)

=> sin theta / cos theta = color(green)(tan theta

Mar 11, 2018

(sin theta csc theta)/cot theta = tan theta.

Explanation:

Firstly, the cosecant function is defined as the inverse sine function:
csc varphi = 1/sin varphi
and the cotangent function as the inverse tangent function: cot varphi = 1/tanvarphi = 1/(sinvarphi/cosvarphi) = cos varphi/sin varphi.

Substituting it into the equation, we have

(sin theta * 1/color(red)(sin theta))/color(red)(cos theta/sintheta)

We know that the product of a number and its inverse is always 1 :

color(red)1/color(red)(costheta/sintheta) = sin theta/cos theta = tan theta.