Homework Help

Prove csc^2 x + sec^2 x = csc^2 x sec^2 xRS shows the 2 sets being multiplied.

user profile pic

islnds | Valedictorian

Posted January 5, 2011 at 6:27 AM via web

dislike 0 like

Prove

csc^2 x + sec^2 x = csc^2 x sec^2 x

RS shows the 2 sets being multiplied.

1 Answer | Add Yours

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 5, 2011 at 7:33 AM (Answer #1)

dislike 2 like

csc^2 x + sec^2 x = csc^2 x * sec^2 x

We will start from the left side and prove the right side.

We know that:

csc(x) = 1/sin(x) ==> csc^2 x = 1/sin^2 x

sec(x) = 1/cos(x) ==> sec^2 x = 1/cos^2 x

We will substitute:

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

Now we will rewrite using the common denominator (sin^2 x*cos^2 x)

==> (cos^2 x + sin^2 x) / (sin^2 x* cos^2 x)

Now we know that sin^2 x + cos^2 x = 1

==> 1 / (sin^2 x *cos^2 x)

==> 1/sin^2 x  *  1/cos^2 x

==> csc^2 x * sec^2 x ...................q.e.d

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes