Question

Use the fundamental identities to simplify the expression. There is more than one correct form of the answer.
7 sec^2 x(1 − sin^2 x)

I have done some work which I am going to add in here in a second but please see what you can get for an answer.

Answer 1

sec^2x = 1 / cos^2 x
and 1 - sin^2 x = cos^2x
so the expression becomes
(7 / cos^2 x) * cos^2 x
= 7

Answer 2

only 7

Answer 3

Okay this is what I have done so far...\[7\sec^2(1-\sin^2x)\]\[7(1+\tan^2x)(-\cos^2x)\]\[(7+7\tan^2x)(-\cos^2x)\]\[-7\cos^2x-7\tan^2xcos^2x\]\[-7\cos^2x-\frac{7\sin^2x}{\cos^2x}\cos^2x\]\[-7\cos^2x-7\sin^2x\]\[-7(\sin^2x+\cos^2x)\]\[-7(1)\rightarrow-7\]Thats what I got, anything wrong with it?

Answer 4

there is a slight error in second line 1 - sin^2 x= cos^2 x (positive)

Answer 5

How is it positive if the identity is\[\sin^2x+\cos^2x=1\]Wouldn't you need to say\[\sin^2x-1+\cos^2x=0 \rightarrow \sin^2x-1=-\cos^2x\]

Answer 6

nvm I wrote it wrong in my notes -_-

Answer 7

I wrote it as sin^2-1 instead of 1-sin^2x

Answer 8

yes - simple error - easily made - none of us are computers!!

Answer 9

Ain't that the truth. Thanks for checking my error.

Answer 10

yw