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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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differentiate tanx

tanx = sinx/cosxapply the quotient rule use the identity cos^x + sin^x = 1 to simplify

Answered by ayaz m. • Maths tutor

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Using a method that is not factorisation, solve the equation (x^2) + 3x -4 = 0. Hence, sketch the curve produced by the equation

One method that could be used to solve the equation is using the quadratic formula given by:x = ( -b ± (b² - 4ac)^0.5) / 2a where ax² + bx + c = 0Substituting our values in...

Answered by Joseph W. • Maths tutor

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Complete the square of the equation below.

Q. Complete the square : x²+ 4x - 12A. Completing the square is putting the given equation into the form (x + a) ² + bFirst, a = the coefficient of x 2so in this case a = ...

Answered by Victoria Y. • Maths tutor

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