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How do I show that (cos^4x - sin^4x) / cos^2x = 1 - tan^2x

Start with the LHS: (cos^4x - sin^4x) / cos^2x Recognise the difference of two squares on the top line, which simplifies to (cos^2x - sin^2x)(cos^2x + sin^2x): (cos^2x - sin^2x)(cos^2x + sin^2x) / cos^2x Bec...
JM
Answered by Jack M. • Maths tutor
20435 Views

Why is the integral of a function the area?

Say you have two functions, A and B, and A is the gradient of B. That is to say, A is as high as B is steep (at any point). Equally, A is as high as the rate of change of B (at any point). Now let’s say we w...
MC
Answered by Madison C. • Maths tutor
3675 Views

integrate cos^2(x)*sin(x)

integral of cos 2 (x)*sin(x) we notice that we can use the spot the ball method here: Guessed integral: cos 3 (x) Differentiated Guessed Integral: -3sin(x)cos 2 (x), therefore our solution is (-1/3)*cos 3 (x)+c
CP
Answered by Cezar P. • Maths tutor
9320 Views

Solve the equation: 5^(2x+1) = 7, giving your answer correct to four decimal places.

First, we take logs of both sides: log(5^(2x+1))=log(7) Now, using the 3rd law of logs (index rule; using the power as the coefficient), we get: (2x+1)log(5)=log(7) i.e. 2x+1 = (log(7))/(log(5)) = 1.20906......
MS
Answered by Mohamad S. • Maths tutor
10132 Views

Why is the derivative of inverse tan(x) 1/(1+x^2)?

This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first princ...
NG
Answered by Neel G. • Maths tutor
7097 Views