Question

Not sure the right approach to solve the identity:
tan3x - tanx = 2sinxsecx

Answer 1

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Answer 2

sorry i meant
tan3x - tanx = 2sinxsec3x

Answer 3

this is a tricky - you might try converting to functions of sin and cos

Answer 4

i've spent a lot of time trying diff techniques, splitting 3x in sinx and cosx components but am getting no where fast!

Answer 5

yeah - i've got a headache trying this one but I've got to go out now. I'll look at it later. Maybe someone else can help meantime. I'd like to see the proof of this one. Meanwhile - the best of luck.

Answer 6

thanks for trying

Answer 7

ok steanson - I've got it
first convert to sin and cos:
sin3x/cos3x -six/cosx
this can be written as
(sin3xcosx - sinxcos3x) / cos3xcosx
by the 'sums and differences of trig ratios formulae:

the numerator = 1/2(sin4x +sin2x) - 1/2(sin4x- sin2x)
which reduces to sin2x which we can write as 2sinxcosx
sowe have:
2 sinxcosx/cos3xcosx

cancelling out cosx

= 2sinx/cos3x

=2sinxsec3x

Answer 8

the rules i referred to are

sinx + siny = 2sin[(x+y/2][cos(x-y)/2]
and
sinx - siny = 2cos[(x+y/2][sin(x-y)/2]

and I used them from' right to left'

A good way to remember these is
eg the first one

'sinx + siny = 2 sin semi sum cos semi difference'

there are similar rules for the sum of differences of cosines.

A higher grade maths book should have them

Answer 9

thanks very much!, i think the reason i struggled is i didn't have those sinx + siny identities given in my text, handy to know!