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Let #sinx=2/3#, how do you show that #f(2x)=-(4sqrt5)/9#?

1 Answer

Mar 14, 2017

see explanation below

Explanation:

#sin x = 2/3#, therefore by using Pythagoras theorem,
#cos x = sqrt 5/3#

if #f(x) = sin x#, then
#f(2 x) = sin 2 x#

#sin 2 x = 2 sin x cos x#

#sin 2 x = 2 * 2/3 *sqrt 5/3#

therefore,
#f (2 x) =sin 2 x = (4 sqrt 5)/9#

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