when simplifying tan²x-sec²x why does it equal 1, not -1?
i do understand how tan²x+1=sec²x (basic identity)
and how you rewrite the equation it turns to
tan²x-sec²x=-1
however when simplifying tan²x-sec²x...
tan²x-sec²x
turned into sine and cosine
=(sin²x/cos²x)-(1/cos²x)
because denominator is same
=(sin²x-1)/cos²x
because sin²x-1=cos²x
=cos²x/cos²x
=1
if tan²x-sec²x=-1
why doesnt my math come up with negitive 1??????
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You are assuming sin²x-1=cos²x. This is false:
sin^2 x + cos^2 x = 1 => sin^2 x - 1 = - cos^2(x). This is the missing minus sign.
your mistake is on the 2nd to last step. You wrote:
because sin^2 x -1 = cos^2 x. This is not an identity, and is not true.
sin^2 x + cos^2 x = 1. Thus sin^2 x - 1 = -cos^2 x
Well, since your using Pythagorean identities, you should know that sin²x + cos²x = 1. Using algebra you should get to sin²x - 1 = - cos²x, not cos²x. Well that's about all i guess.
negative with an "a"
because sin² x - 1 = –cos² x
the identity is sin² x + cos² x = 1, so 1 - sin² x = cos² x
and when you reverse the order of the subtraction you reverse the sign of the answer.
Pythagorean identity
[sin(x)]^2 + [cos(x)]^2 = 1
Divide everything by [cos(x)]^2 to get
[tan(x)]^2 + 1 = [sec(x)]^2
Move [sec(x)]^2 to the left and 1 to the right of the equal sign to get
[tan(x)]^2 - [sec(x)]^2 = -1