2007-05-25 05:06:50 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Do you mean 1 + tan^@ = sec^2@?
To do this, write everything in terms of sines and cosines, then apply the pythagorean identity...
Since tan = sin/cos and sec = 1/cos, write it as...
1 + (sin^2 @/ cos^2 @) = 1/cos^2 @
Now write the 1 as cos^2 @ / cos^2 @:
cos^2 @ / cos^2 @ + sin^2 @ / cos^2 @ = 1/cos^2 @
See the pythagorean identity lurking on the left side? Put it together and you get
1/cos^2 @ 1/cos^@ and there you have it.
This online text editor isn't much good for writing stuff like this, but if you try writing it out yourself in standard notation you'll get it. Once you understand it, you can do it. Good luck!
2007-05-25 05:09:58 · answer #1 · answered by Joni DaNerd 6 · 0⤊ 1⤋
L.H .S = 1 + tan^2 0 = 1 + sin^2 0 / cos ^2 0
= ( cos^2 0 + sin^2 0 ) / cos^2 0
= 1 / cos^2 0
= sec^2 0 = R.H.S
2007-05-25 05:13:01 · answer #2 · answered by muhamed a 4 · 1⤊ 0⤋
To prove:-
1 + tan²x = sec²x
LHS
= 1 + sin²x / cos²x
= (cos²x + sin²x) / cos²
= 1 / cos²x
= sec²x
RHS = sec²x
LHS = RHS
Thus 1 + tan²x = sec²x
2007-05-25 20:42:44 · answer #3 · answered by Como 7 · 0⤊ 0⤋