Homework Help

For all possible values of variable x, what is the result of the sum?...

user profile pic

jeuxdesfou | Student, Undergraduate | Honors

Posted March 24, 2011 at 6:52 PM via web

dislike 1 like

For all possible values of variable x, what is the result of the sum?

(1+sin^2x)/(2+cot^2x)+(1+cos^2x)/(2+tan^2x)=

Tagged with math, sum, variable

1 Answer | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted March 24, 2011 at 7:04 PM (Answer #1)

dislike 0 like

We know, from Pythagorean identity, that:

1 + (tan x)^2 = 1/(cos x)^2

1 + (cot x)^2 = 1/(sin x)^2

We'll re-write the denominators:

1 + 1 + (cot x)^2 = 1 + 1/(sin x)^2

2 + (tan x)^2 = 1 + 1 + (tan x)^2 = 1 + 1/(cos x)^2

We'll re-write the expression:

[1+(sinx)^2]/(2+(cot x)^2)+[1+(cos x)^2]/(2+(tan x)^2)=

[1+(sinx)^2]/(1 + 1/(sin x)^2) + [1+(cos x)^2]/(1 + 1/(cos x)^2) =

[1+(sinx)^2]/[((sinx)^2 + 1)/(sin x)^2] + [1+(cos x)^2]/[((cos x)^2 + 1)/(cos x)^2] =

(sin x)^2 + (cos x)^2 = 1

The required value of the given sum is S = 1.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes