Question

use a double-angle formula to find the exact value of cos2u when sinu=5/13 , where pi/2<u<pi

So far I went
cos2u=1-sin^2
=1-2(25/169)
=1-(50/169)

Answer 1

Correct answer but you also can write :

cos ( 2 u ) = cos ^ 2 ( u ) - sin ^ 2 u

In this case :

sin ( u ) = 5 / 13

sin ^ 2 ( u ) = ( 5 / 13 ) ^ 2 = 25 / 169

cos ^ 2 ( u ) = 1 - sin ^ 2 ( u ) =

1 - 25 / 169 = 169 / 169 - 25 / 169 = 144 / 169


cos ( 2 u ) = cos ^ 2 ( u ) - sin ^ 2 u =

144 / 169 - 25 / 169 = 119 / 169

Answer 2

correct. How can you be stuck there? Surely by the time you have learned trigonometry, you know how to work with fractions ... ?

hint: 1 = 169/169

Answer 3

OH my god I feel very dumb because 1/1 is 169/169 Thank you !