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Using the identity cos(A+B)= cosAcosB-sinAsinB, prove that cos2A=1-2sin^2A.

Use cos(A+B)=cosAcosB-sinAsinB and let A=B so cos(A+A)=cosAcosA-sinAsinA this means cos(2A)=cos²A-sin²A and since cos²A+sin²A=1, cos²A=1-sin²

Answered by Rebecca F. • Maths tutor

21773 Views

A curve has the equation: x^3 - x - y^3 - 20 = 0. Find dy/dx in terms of x and y.

x³ - x - y³ - 20 = 0 Find dy/dx. Differentiate with respect to x.
3x² - 1 - 3y²(dy/dx) = 0Therefore: dy/dx = (3x

Answered by Karishma P. • Maths tutor

3576 Views

Alex designs a game for people to play, using two fair five-sided spinners. A person wins the game when both spinners land on the same letter. People pay 40p for each game they play. The prize for a win in £1. Is she likely to raise money?

In order to raise money, we need the average number of wins to be smaller than the average number of losses by at least a factor of 0.4.
The average number of wins will be the number of games multipl...

Answered by Megan L. • Maths tutor

3220 Views

Sam works for £14 per hour. When Sam works more than 8 hours a day, he is paid overtime for each hour he works more than 8 hours at 1½ times his normal rate of pay. Sam worked for 12 hours. Work out the total amount of money Sam earned.

Find the wage received from normal rate= 8x14=112. We then find the wage received from working overtime by finding the number of extra hours worked (12-8=4) multiplied by the overtime wage of (1½ x14= 1.2...

Answered by Joseph C. • Maths tutor

5605 Views

Find the exact gradient of the curve y = ln(1-cos 2x) at the point with x-coordinate π/6.

The gradient to the curve is given by the derivative of the function y = f(x) = ln(1 - cos 2x). This function is a composition of two other functions so we need to use the chain rule to find the derivativ...

Answered by Archie R. • Maths tutor

7087 Views