Question

Integrate 1/ cos^2 (x)

Answer 1

1/cos = sec

Answer 2

\[\int\limits_{}^{}1/\cos^2(x) dx =\int\limits_{}^{}\sec^2(x) dx\]

Now just integrate

Answer 3

@jychay2


Got it ?

Answer 4

ya,I got it.Thx^^

Answer 5

This is just a matter of memorizing the derivatives and definitions of certain trigonometric functions.

Answer 6

@jychay2

So what should be the answer ?

Answer 7

tany. Am i right?

Answer 8

oh,srry.Its tanx

Answer 9

No you are wrong the answer would be


\[\tan(x)+c\]

c is very imp,if you miss it you get no marks+your answer goes wrong.

Answer 10

@jychay2

Got it ?

Answer 11

Oh,ya! Forgot the c,constant. Thx for the correction

Answer 12

Your'e welcome :)

Answer 13

Yeah, saying the answer is \(\tan(x)\) is basically saying that the answer is \(\tan(x) + 0\), which is also like saying the answer is \(\tan(x)+103\). It's like saying the population is \(100,021\) just as \(4\) people enter the city. That's why they are so particular about it. But it is kinda funny too.

Answer 14

Consider that you can derive the result sec^2(x) as the derivative of tanx simply because you know the derivatives of sine and cosine, which is essentially what tangent is. I suggest everyone does this at least once in their life.

Answer 15

Lol, boring exercise no?
\[\frac{d}{dx} \frac{\sin(x)}{\cos(x)}=\frac{\cos^2(x)+\sin^2(x)}{\cos^2(x)}=\sec^2(x)\]