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Quick Trig question? Trig Identities!?
Okay so I have to make this : sec^2x-sin^2x resemble this: cos^2x+tan^2x
Using trig identities
I did many other problems similar to this but, for some odd reason I am having trouble with this question.
Steps would be most gratefull!
Thank you!
1 Answer
- morganLv 78 years agoFavorite Answer
Given:
sec^2(x) - sin^2(x) = cos^2(x) + tan^2(x)
Would it be sufficient to show that the
two sides are equal? That's easier than
just converting the left side to be the
right side.
Add sin^2(x) to both sides:
sec^2(x) = cos^2(x) + tan^2(x) + sin^2(x)
Subtract tan^2(x) from both sides:
sec^2(x) - tan^2(x) = cos^2(x) + sin^2(x)
Apply the identity: sin^2 + cos^2 = 1
sec^2(x) - tan^2(x) = 1
Multiply both sides by cos^2(x)
sec^2(x)*cos^2(x) - tan^2(x)*cos^2(x) = cos^2(x)
1 - sin^2(x) = cos^2(x)
Add sin^2(x) to both sides of the equation:
1 = sin^2(x) + cos^2(x)
Apply the identity sin^2 + cos^2 = 1
1 = 1
done.