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Integrate sin^2(x) with respect to x

use trigonometric identities i.e. Cos(2x) = Cos 2 (x) - Sin 2 (x) (a) Cos 2 (x) + Sin 2 (x) = 1 (b) Therefore: Cos 2 (x) = 1 - Sin 2 (x) (c) Combining (a) and (c) we achieve Cos(2x) = 1 - 2 Sin 2 (x) Rearran...
OL
Answered by Oscar L. • Maths tutor
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Given that 2cos(x+50)°=sin(x+40)° show tan x° = tan 40°/3

The formulae for the sum the sine and cosine of two angles are: 2(cos x°cos 50°- sin x°sin 50°)= sin x°cos 40°+cos x°sin 40°cos 50°= sin 40°sin 50° = cos 40° Therefore, 2 cos x°sin 40°- 2 sin x°cos 40° = sin...
PT
Answered by Prashasti T. • Maths tutor
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Integrate x * sin(x) with respect to x by using integration by parts

The general formula for integration by parts to integrate something of the form u * v' is: u * v - (integral)[ (u' * v) dx ] . Thus we first need to write x * sin(x) in the form u * v' . Lets pick u = x and ...
JW
Answered by Jamie W. • Maths tutor
6244 Views

write 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) in terms of cos(2x) and sin(2x)

We use the following double angle formulae cos(2x) = cos^2(x) - sin^2 (x) and sin(2x) = 2sin(x)cos(x) to see that 2(sin^2(x)- cos^2(x)) + 6 sin(x) cos(x) = -2-(sin^2(x)+ cos^2(x)) + 3*2 sin(x) cos(x) = -2cos...
NR
Answered by Nicola R. • Maths tutor
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Factorise and solve x^2 -4x -12=0

x 2 - 4x -12 is a quadratic equation with a general formula. It can be factorised by into brackets and solved.By looking at the equation, the last term is negative so one number in the factorised form must b...
MM
Answered by Mitchel M. • Maths tutor
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