I did put the equation as

then I used the formula

and simplified it.

hence it was proved.

]]>Especially as I make sign mistakes all the time.

2-4sin^2θ+3sin^4θ-sin^6θ=1

Did you manage this bit?

Bob

]]>thanks for the correction, the answer came out easily.:D

I spent 2 hrs around it and wasted so many sheets of paper, phew!!]]>

Bob

]]>use the G.M. formula if tanθ is the G.M. between sinθ and cosθ then tanθ=sqroot(sinθ*cosθ) then u easily get sinθ=cos^3 θ so just post the expression clearly so we can work it out]]>

so for your question

Now what I suggested will work.

Bob

]]>If θ≠n*pi and tanθ is the geometric mean between sinθ and cosθ , then prove that 2-4sin^2θ+3sin^4θ-sin^6θ=1

geometric mean was given what I mentioned and the solution solved the above in just a single line saying

after that sinθ was taken in terms of cos^3θ and the question was solved easily.

But I couldn't get how this result was obtained..

]]>I'm sorry; I thought this would come out easily. Changing the tan is the standard thing I would do for one like this. Then everything is in terms of sine and cos so it should have worked.

But I cannot do it either. Below I have shown the graphs for (i) tan and root(sin - cos) and then for (ii) sin and cos cubed.

The first pair only cross in positive real numbers and twice in each 2pi repeat of the graphs. The second pair cross once only in positive values in each 2pi repeat. And nowhere near the same value of x (theta). So it would seem that this cannot be shown for real numbers. Odd.

Is it possible there's a 'typo' somewhere?

Bob

]]>Put tan = sin/cos and square the equation.

Bob

]]>prove that:-

]]>