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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.

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.

Thank you, I knew I needed to use the compound angle formulae but I just couldn't understand it. Cheers

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 - y_{1} = m(x - x_{1} )

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.

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 - y

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.

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.

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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