dy/dx of tan x is sec^2 x is there another way of writing sec^2 x?
sec^2 x
= (secx)^2
= 1/(cosx)^2
= 1/(1 - sin^2 x)
does that help?
Yes
(Tan2x-√3)(cot3x+1)
Yes, there is another way of representing sec^2 x. The expression sec^2 x can be written as (1/cos^2 x).
To understand how this alternative expression is derived, let's begin with the definition of sec x. The secant of an angle is defined as the reciprocal of the cosine of that angle. Mathematically, sec x = 1/cos x.
Now, to find an alternative expression for sec^2 x, we need to square both sides of the above equation.
(sec x)^2 = (1/cos x)^2
Simplifying further, we get:
sec^2 x = (1/cos x)^2
Now, in the denominator, when we square a fraction (1/cos x)^2, we square both the numerator and the denominator separately. This results in:
sec^2 x = (1^2)/(cos^2 x)
And since 1^2 is just 1, the expression becomes:
sec^2 x = 1/(cos^2 x)
Therefore, another way of writing sec^2 x is (1/cos^2 x).
Hence, the derivative of tan x, which is sec^2 x, can also be represented as (1/cos^2 x).