Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 4 | A Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
?
Date Posted: 3 years ago
Views: 569
sin 3A - sin A - cos 2A
= sin (2A + A) - sin A - (1 - 2 sin² A)
= sin 2A cos A + cos 2A sin A - sin A - 1 + 2 sin² A
= (2 sin A cos A) cos A + (1 - 2 sin² A) sin A - sin A + 2 sin² A - 1
= 2 sin A cos² A + sin A - 2 sin³ A - sin A + 2 sin² A - 1
= 2 sin A (1 - sin² A) - 2 sin³ A + 2 sin² A - 1
= 2 sin A - 2 sin³ A - 2 sin³ A + 2 sin² A - 1
= 2 sin A - 4 sin³ A + 2 sin² A - 1
= sin (2A + A) - sin A - (1 - 2 sin² A)
= sin 2A cos A + cos 2A sin A - sin A - 1 + 2 sin² A
= (2 sin A cos A) cos A + (1 - 2 sin² A) sin A - sin A + 2 sin² A - 1
= 2 sin A cos² A + sin A - 2 sin³ A - sin A + 2 sin² A - 1
= 2 sin A (1 - sin² A) - 2 sin³ A + 2 sin² A - 1
= 2 sin A - 2 sin³ A - 2 sin³ A + 2 sin² A - 1
= 2 sin A - 4 sin³ A + 2 sin² A - 1
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Basically we need to break the entire expression to an expression involving only powers of sin A.
In other words, we are not allowed to retain other terms like cos A or sin 3A in our final expression.
In other words, we are not allowed to retain other terms like cos A or sin 3A in our final expression.
Date Posted:
3 years ago
Generally , terms with negative sign shouldn't be put as the leftmost
In this situation I decided to arrange the order in a decreasing power of sin x as per regular polynomials, because a typical polynomial is expressed in descending powers.
Ascending powers does the job here well (negative sign isn't in front and terms are in order.)
360 Tutoring Program