Question #bb0b9

1 Answer
Nghi N.
Oct 28, 2015

Find sin 2x; cos 2x; and tan 2x

Explanation:

#(sin x - cos x = 1/5)^2#
#sin^2 x + cos ^2 x - 2sin x.cos x = 1/25#
Since #(sin^2 x = cos^2 x = 1)# and #(2sin x.cos x = sin 2x)#, therefor:
#1 - sin 2x = 1/25#
#sin 2x = 1 - 1/25 = 24/25#
#cos^2 2x = (1 - 576/625) = (625 - 576)/625 = 49/625# -->
--> #cos 2x = 7/25.#
#tan 2x = (sin 2x)/(cos 2x) = (24/25)(25/7) = 24/7#

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