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How do I show that (cos^4x - sin^4x) / cos^2x = 1 - tan^2x

Start with the LHS: (cos^4x - sin^4x) / cos^2x Recognise the difference of two squares on the top line, which simplifies to (cos^2x - sin^2x)(cos^2x + sin^2x): (cos^2x - sin^2x)(cos^2x + sin^2x) / cos^2x Bec...
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Answered by Jack M. • Maths tutor
20456 Views

£3000 is invested for 2 years at 3.8% per annum compound interest. What is the total interest earned over the 2 years?

We can use the following formula: Amount after n years' compound interest = Initial amount x (1 + r) n r = The interest rate in decimal form. n = Number of years. Simply plug the values into our formula: £30...
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Answered by Arisera T. • Maths tutor
10332 Views

Farmer Joe has a rectangular pen to hold his animals. The pen’s length is 5 meters longer than the width. The pen’s area is 84 meters. Find it’s width.

Step 1 define the variables: L stands for the length, W stands for the width Step 2 write what we know algebraically: Since the length is 5 meters longer than the width we have L = W + 5. Finally, the area i...
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Answered by Omar B. • Maths tutor
3557 Views

Find all three roots of the cubic: 2x^3 +5x^2 - 22x +15=0.

First try a trivial solution, x=0: doesn't work. Then try x=1 this does work so (x-1) is a factor of the cubic. Through algebraic factorisation (2x 2 +7x-15) comes out as a factor. This can be factorised int...
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Answered by Stanley W. • Maths tutor
3892 Views

What do I need the Pythagoras theorem for?

As an example you can use it to calculate the length of the hypotenuse in a triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides. As a formula a^2 + b^2 = c^2
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Answered by Fabienne D. • Maths tutor
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