Note that for sec²(x) - tan²(x) = 1, we have:
-tan²(x) = 1 - sec²(x)
tan²(x) = sec²(x) - 1
Rewrite the expression as:
∫ (sec²(x) - 1) dx
= ∫ sec²(x) dx - ∫ 1 dx
Finally, integrate each expression to get:
tan(x) - x + K where K is the arbitrary constant
Chat with our AI personalities
integral of radical sinx
tan(x) + C d/dx tan(x) = d/dx (sin(x))/(cos(x)) = (sin^2(x)+cos^2(x))/(cos^2(x)) = 1/(cos^2(x)) = sec^2(x) NEVER FORGET THE CONSTANT!
The indefinite integral of (1/x^2)*dx is -1/x+C.
The integral of sec(x) with respect to x is ln|sec(x) + tan(x)| + C, where C is the constant of integration. This result can be derived using integration techniques such as substitution or integration by parts. The integral of sec(x) is a common integral in calculus and is often used in trigonometric integrals.
cot2x-tan2x=(cot x -tan x)(cot x + tan x) =0 so either cot x - tan x = 0 or cot x + tan x =0 1) cot x = tan x => 1 / tan x = tan x => tan2x = 1 => tan x = 1 ou tan x = -1 x = pi/4 or x = -pi /4 2) cot x + tan x =0 => 1 / tan x = -tan x => tan2x = -1 if you know about complex number then infinity is the solution to this equation, if not there's no solution in real numbers.