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How can I demonstrate that (sin(T)+cos(T))(1-sin(T)cos(T))=(sin(T))^3+(cos(T))^3

You first develop the expression on the left side of the equation:(sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)-sin^2(T)cos(T)+cos(T)-sin(T)cos^2(T)=sin(T)(1-cos^2(T))+cos(T)(1-sin^2(T))Now, you will need to use th...
TC
Answered by Tabea C. • Maths tutor
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Find the integral of e^3x/(1+e^x) using the substitution of u=1+e^x

Differentiate U with respect to x to find dx in terms of du and substitute into the integral so that it is in terms of du, then using e^3x = (e^x)^3 and u = 1+e^x subsitute u in for x and simplify the integr...
CF
Answered by Cory F. • Maths tutor
5582 Views

dx/dt = -5x/2, t>=0. Given that x=60 when t=0, solve the differential equation, giving x in terms of t.

dx/dt = -5x/2 to solve this we must firstly separate the variables ∫2/x dx = -∫5 dt t hen we solve the integrals using basic integration formulae 2lnx = -5t+c. When it comes to the exam, many students forget...
KS
Answered by Kulveer S. • Maths tutor
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Why do I have to study maths?

Maths is very important in real life. You use it day to day from basic addition and subtraction to working out percentage discounts in shops. Some of the more complex maths like algebra is used in fields lik...
JP
Answered by Jack P. • Maths tutor
3354 Views

Expand and simplify (x-4)(2x+3y)^2

( x -4) x (2 x +3 y ) 2 (x-4) x (4x 2 +12xy +9y 2 ) 4x 3 +12x 2 y + 9xy 2 -16x 2 -48xy - 36y 2 finished.
JT
Answered by James T. • Maths tutor
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