Trig identity question.?
- grunfeldLv 71 decade agoFavorite Answer
LHS = 1 + tan^2 x
LHS = (cos^2 x + sin^2 x) / cos^2 x
LHS = 1 / cos^2 x
LHS = RHS
- 1 decade ago
Take the Pythagorean Identity and divide both sides by cos^2 x.
Pythagorean Identity: (sin^2 x +cos^2 x = 1).
- David NuttallLv 61 decade ago
I am assuming you want to prove this identity. First, express everything in terms of sine and cosine.
LS = 1 + tan^2(x)
LS = 1 + sin^2(x) / cos^2(x)
RS = 1 / cos^2(x)
Next I when I start seeing sin^2 and cos^2 in a proof, I start thinking of using the Pythagorean identity. sin^2(x) + cos^2(x) = 1, for all x.
To perform the addition on the left side, I need a common denominator, which in this case is cos^2(x).
LS = cos^2(x)/cos^2(x) + sin^2(x) / cos^2(x)
LS = [cos^2(x) + sin^2(x) ] / cos^2(x)
Apply the Pythagorean identity to the numerator.
LS = 1 / cos^2(x)
LS = RS