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Express 3sin(2x) + 5cos(2x) in the form Rsin(2x+a), R>0 0<a<pi/2

Start by expanding out Rsin(2x+a) using the addition formula for sin, sin(A+B) = sin(A)cos(B)+cos(A)sin(B). Substituting 2x = A and a= b, we get that Rsin(2x+a) = R(sin(2x)cos(a) + cos(2x)sin(a)) = Rcos(a...

Answered by Michael F. • Maths tutor

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Explain how the theme of love is presented in Shakespeare's "Much Ado About Nothing"

This is an essay question that could come up in A Level based on the syllabus' I have looked at; there is not time or space to write out the full essay here, so I have gone for three key bullet points I w...

Answered by Nathan T. • English tutor

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Solve the simultaneous equations: y=x+1, x^2+y^2=13

We already have an expression for y, so we can substitute this in:x²+(x+1)²=x²+(x+1)(x+1) = x²+x²+2x+1=2x²+2x+1 and hence 2x²+2...

Answered by Lauren C. • Maths tutor

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Using trigonometric identities, show that (cos(x) + sin(x))^2=1+sin(2x)

First being by expanding the brackets of the formula on the left: (cos(x) + sin(x))² = (cos(x) + sin(x))*(cos(x) + sin(x)) = cos²(x)+2cos(x)sin(x)+sin²(x).Now we must use...

Answered by • Maths tutor

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