Show that 2cos^2(x) = 2 - 2sin^2(x) and hence solve 2cos^2(x) + 3sin(x) = 3 for 0<x<180

You can rearrange the equation to get 2cos^2(x)+2sin^2(x) = 2. This can be factorised to get cos^2(x) + sin^2(x) = 1 which is a known identity. We can use the fact that 2cos^2(x) = 2sin^2(x) - 2 and substitute this into the equation. This will give the equation 2sin^2(x) - 2 + 3sin(x) = 3. Rearranging you can get the equation into the form 2sin^2(x) + 3sin(x) - 5 = 0. From here we can substitute u = sin(x) to get the equation 2u^2 + 3u -5 = 0. You can then solve this quadratic using the quadratic formula to get that u = 1 or u = -5/2. Subbing sin(x) back in for u you get that sin(x) = 1 or sin(x) = -5/2. You can ignore the sin(x) = -5/2 as -1 < sin(x) < 1. This leaves that sin(x) = 1. Now to find the values of x between 0 < x < 180. You know that sin(90) = 1 or you can use the arcsin(x) function on your calculator to get the value 90 so you have found that x = 90.

Related Further Mathematics GCSE answers

All answers ▸

What is the distance between two points with x-coordinates 4 and 8 on the straight line with the equation y=(3/4)x-2


A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.


How do I find the limit as x-->infinity of (4x^2+5)/(x^2-6)?


In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences