Explain why sec^2angle-1-tan^2angle=0

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should come up with the substitution: `alpha ` = angle.

You need to remember that secant function is the reverse of cosine angle, hence `sec alpha = 1/(cos alpha) =gt sec^2 alpha = 1/(cos^2 alpha).`

You need expand the tangent function in a fraction such that:

`tan alpha = sin alpha/cos alpha =gt tan^2 alpha = (sin^2 alpha)/(cos^2 alpha)`

You need to write the equation in the new form such that:

`1/(cos^2 alpha) - 1 - (sin^2 alpha)/(cos^2 alpha) = 0`

You need to add 1 both sides such that:

`(1 - sin^2 alpha)/(cos^2 alpha) = 1`

You need to remember the basic trigonometric formula such that:

`sin^2 alpha + cos^2 alpha = 1 =gt cos^2 alpha = 1 - sin^2 alpha`

Hence, substituting `1 - sin^2 alpha ` by `cos^2 alpha`  yields:

`(cos^2 alpha)/(cos^2 alpha) = 1 =gt 1 = 1`

`` This last line establishes the identity `sec^2 alpha - 1 -tan^2 alpha =0.`

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question