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Prove that (sinx + cosx)^2 = 1 + 2sinxcosx

Starting on the left hand side we can expand out the brackets to get: (sinx + cosx)(sinx + cosx) sin 2 x+sinxcosx+sinxcosx+cos 2 x Grouping together the like terms we can rearrange it to be: sin 2 x + cos 2 ...
AG
Answered by Adam G. • Maths tutor
12523 Views

How do you integrate ln(x)?

Tricky. Definitely can't do it by inspection (we don't know any fuction that just differentaties to ln(x)), it's not like we've really got anything to substitute u for if we wanted to do it by substitution a...
RG
Answered by Ross G. • Maths tutor
103143 Views

Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(x)

The first thing we notice is that this differential equation is seperable, meaning we can get all of our y's on the left with a dy and all of our x's on the right with a dx. Doing this by multiplying both si...
RG
Answered by Ross G. • Maths tutor
13165 Views

s^2 - 2s - 24 = 0

s 2 ​ - 18s = 0(s + 4)(s - 6) = 0s = -4 s = 6
NP
Answered by Natasha P. • Maths tutor
4385 Views

Prove that (2n+3)^2-(2n-3)^2 is a multiple of 8 for positive integer values of n

To prove that (2n+3) 2 -(2n-3) 2 is a multiple of 8 we are going to deal with the first bracket and then the second bracket. When a bracket has 2 next to it, this means that you multiplying the bracket, by t...
SD
Answered by Sioned D. • Maths tutor
25055 Views