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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)
sin²x+sinxcosx+sinxcosx+cos²x
Grouping together the like terms we can ...

Answered by Adam G. • Maths tutor

11384 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 substitu...

Answered by Ross G. • Maths tutor

95851 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 b...

Answered by Ross G. • Maths tutor

12656 Views

s^2 - 2s - 24 = 0

s² - 18s = 0(s + 4)(s - 6) = 0s = -4 s = 6

Answered by Natasha P. • Maths tutor

4077 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)²is a multiple of 8 we are going to deal with the first bracket and then the second bracket. When a bracket has ²next to it, this means that ...

Answered by Sioned D. • Maths tutor

23993 Views