Trigonometric Identities

Given cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

I was able to evaluate cosec A - cot A:
cosec^2 A - cot^2 A = 1
(cosec A - cot A)(cosec A + cot A) = 1
(cosec A - cot A) x 3 = 1
Therefore, (cosec A - cot A) = 1/3

However, I was not able to evaluate cos A.

The answer should come up to cos A = 4/5.

Multiply both sides of the equation by to get .

Now square both sides to get

So .





We get the two solutions

-1 is an extraneous solution since it makes cot A undefined.

Use what you were given:



.....1





.........2

Substitute 2 in 1.