Question

intigrate with respect to x
1/cos^2x(sin^2x + cos^2x) dx
​

Answer 1

we know that

Sin^2(x ) + cos^2(x) = 1

and

1/cos^2x = sec^2x

Given

$\int \frac{ 1 }{ { \cos(x) }^{2} ( { \sin(x) }^{2} + { \cos(x) }^{2} )} dx$

Now on using formula

$\int { \sec(x) }^{2} dx \\ \tan(x) + c$

Answer 2

Answer:

tan(x)+C

Step-by-step explanation:

$\int \frac{dx}{ { \cos(x) }^{2}( { \sin(x) }^{2} + { \cos(x) }^{2} ) } \\ \int \frac{dx}{ { \cos(x) }^{2} (1)} \\ \int \frac{dx}{ \frac{1}{ { \sec(x) }^{2} } } \\ \int { \sec(x) }^{2} dx \\ \tan(x) + c$