QR2 from achiever question

[rockets32]

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hey guys I was wondering if you can help me with this problem from achiever. on QR2 #39, how do they end up with -cos2 theta in the numerator in the third step? I know sin2 theta + cos2 theta will give you one, but how does the other factor work out?

thanks in advance

 

[CanalRooting]

hey guys I was wondering if you can help me with this problem from achiever. on QR2 #39, how do they end up with -cos2 theta in the numerator in the third step? I know sin2 theta + cos2 theta will give you one, but how does the other factor work out?

thanks in advance

That's because:

cos 2 theta = cos^2 theta - sin^2 theta {Standard Identity of Trig}

making:

- cos 2 theta = - cos^2 theta + sin^2 theta

==> sin^2 theta - cos^2 theta = - cos 2 theta