Verify the identity algebraically. Use a graphing utility to check your result graphically. (Simplify at each step.)

Question

8 cot²(y)(sec²(y) − 1) = 8

8 cot2(y)(sec2(y) − 1) = 8 cot2(y) (?) = 8

Answer 1

Remember the Trig Identity 1 + tan²(x) = sec²(x)

We can subtract 1 from both sides to get tan²(x) = sec²(x) - 1

Therefore,

8cot²(y)(sec²(y) − 1) =

8cot²(y)tan²(y) [using the substitution above]

Note that cot²(y) = 1 / tan²(y)

Therefore,

8cot²(y)tan²(y) = 8(1) = 8