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Since sin(theta) = 1/cosec(theta) the first two terms simply camcel out and you are left with 1 divided by tan(theta), which is cot(theta).
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Suppose triangle ABC is right angled at C. Suppose you are given that the angle at B is theta. Thenif you know the length of AB (the hypotenuse), thenBC = AB*cos(theta) andAC = AB*sin(theta)if you know the length of BC, thenAB = BC/cos(theta) andAC = BC*tan(theta)if you know the length of AC, thenAB= AC/sin(theta) andBC = AC/tan(theta)
SOH CAH TOA is a way of remembering what the functions sin, cos, & tan mean in a right angle triangle. With a triangle with one of the acute angles labelled (theta) the longest side H (Hypotenuse), the side opposite the labelled angle O, and the short side closest to the angle A (Adjacent) SOH ->SIN(Theta)=0/H CAH ->COS(Theta)=A/H TOA ->TAN(Theta)=O/A
Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1