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secondary 3 | A Maths
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choot
Choot

secondary 3 chevron_right A Maths chevron_right Singapore

help pls i tried but cant seem to understand help asap thankyousomuchh:)

Date Posted: 1 week ago
Views: 20
Eric Nicholas K
Eric Nicholas K
1 week ago
sin 3x
= sin (2x + x)
= sin 2x cos x + cos 2x sin x

(using the addition formula for sin (A + B))

= (2 sin x cos x) cos x + (1 - 2 sin²x) sin x

(using the double angle formula for sin 2A and the all-sine form of the double angle formula for cos 2A)

= 2 sin x cos²x + sin x - 2 sin³x
= 2 sin x (1 - sin²x) + sin x - 2 sin³x

(using the identity sin²x + cos²x = 1 to express our result in sines only)

= 2 sin x - 2 sin³x + sin x - 2 sin³x
= 3 sin x - 4 sin³x

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Danny Low
Danny Low's answer
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Hope this helps