# What is the slope of the line normal to the tangent line of #f(x) = sec^2x-sin^2x # at # x= (pi)/12 #?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the slope of the line normal to the tangent line of (f(x) = \sec^2x - \sin^2x) at (x = \frac{\pi}{12}), we first need to find the derivative of (f(x)) and evaluate it at (x = \frac{\pi}{12}) to get the slope of the tangent line. Then, we can find the negative reciprocal of this slope to get the slope of the line normal to the tangent line. The derivative of (f(x)) is (f'(x) = 2\sec^2x\tan x + 2\sin x\cos x), and evaluating it at (x = \frac{\pi}{12}) yields (f'\left(\frac{\pi}{12}\right) = 2\sec^2\left(\frac{\pi}{12}\right)\tan\left(\frac{\pi}{12}\right) + 2\sin\left(\frac{\pi}{12}\right)\cos\left(\frac{\pi}{12}\right)). After calculating this, we take the negative reciprocal of the result to find the slope of the line normal to the tangent line.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the slope of a line tangent to the curve #3y^2-2x^2=1#?
- How do you use the definition of a derivative to find the derivative of #G(t)= (4t)/(t+1)#?
- How do you find the derivative of #y = sqrt(x + 1)# using the limit definition?
- How do you use the limit definition of the derivative to find the derivative of #f(x)=-4#?
- What is the equation of the line normal to #f(x)=x^2-3x # at #x=2#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7