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    Hello, could you help me with these two questions please? I've tried to do them myself but I just can't get my head around them.

    PS π is pie

    First question:

    The tangent to the curve y=2xtanx at the point where x=π/4 meets the y-axis at the point P.

    Find the y-coordinate of P in the form kπ² where k is a rational constant to be found.

    Second question:

    Show that sin(x+30) + sin(x-30) = asinx where a is a constant to be found.

    Thank you very much in advance.
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    second question - use the compound angle formulae

    sin(x+30) = sinxcos30 + cosxsin30

    sin(x-30) = sinxcos30 - cosxsin30

    thus sin(x+30) + sin(x-30) = 2sinxcos30

    cos30 = root3/2

    therefore

    a= root3
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    Thank you, I knew I needed to use the compound angle formulae but I just couldn't understand it. Cheers
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    The tangent to the curve y=2xtanx at the point where x=π/4 meets the y-axis at the point P.

    Find the y-coordinate of P in the form kπ² where k is a rational constant to be found

    Yo!

    Ok. Tangent to the curve at x = π/4. We need to know the gradient at this point. We know that the point (π/4, π/2) is on the line.


    dy/dx = 2x(sec²x) + 2tanx

    x = π/4 => dy/dx = π + 2

    So we have a point on the line and it's gradient!

    y - y1 = m(x - x1 )

    y - π/2 = (π + 2)(x - π/4)

    y = (π + 2)x - π²/4 - π/2 + π/2

    y = (π + 2)x - π²/4

    => y-intercept = π²/4.....k = 1/4 which is rational and constant so that seems good.
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    Thanks for the help but I get a bit lost at this part

    y - y1 = m(x - x1 )

    y - π/2 = (π + 2)(x - π/4)

    y = (π + 2)x - π²/4 - π/2 + π/2

    y = (π + 2)x - π²/4

    ...with the y1's and x1's, I understand you're trying to work at the c part of y=mx+c but I'm not sure how you did that.
 
 
 
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