Ask Singapore Homework?

Upload a photo of a Singapore homework and someone will email you the solution for free.



Question

secondary 3 | A Maths
One Answer Below

Anyone can contribute an answer, even non-tutors.

Answer This Question
li ning
Anonymous

secondary 3 chevron_right A Maths chevron_right Singapore

how to prove the following identity pls help thank you

Date Posted: 4 months ago
Views: 11
J
J
4 months ago
① Change cos²x - sin²x to (cosx + sinx)(cosx - sinx).

(Property applied here is a² - b² = (a + b)(a - b) )

② Change 1 + 2sinxcosx to sin²x + cos²x + 2sinxcosx, (use property cos²x + sin²x = 1)
which = (sinx + cosx)²

(Property used here is (a + b)² = a² + 2ab + b²)

③ Then cancel out (cosx + sinx) on both the numerator and denominator. This leaves (cosx + sinx)/(cosx - sinx)


④ Divide both numerator and numerator by cosx.

This leaves (1 + sinx/cosx)/(1 - sinx/cosx)

, which equals (1 + tanx)/(1 - tanx)
J
J
4 months ago
Alternatively, divide both numerator and denominator by cos²x first.

(1 + 2sinxcosx)/(cos²x - sin²x)

= (sin²x + cos²x + 2sinxcosx)/(cos²x - sin²x)

= (sin²x/cos²x + cos²x/cos²x + 2sinxcosx/cos²x)/(cos²x/cos²x - sin²x/cos²x)

= (tan²x + 2sinx/cosx + 1)/(1 - tan²x)

= (tan²x + 2 tanx + 1)/( (1 + tanx)(1 - tanx) )

= (tanx + 1)² / ( (1 + tanx)(1 - tanx) )

= (tanx + 1)/(1 - tanx)
li ning
Li Ning
4 months ago
thank youu
J
J
4 months ago
Welcome

See 1 Answer

done {{ upvoteCount }} Upvotes
clear {{ downvoteCount * -1 }} Downvotes
Eric Nicholas K
Eric Nicholas K's answer
3937 answers (Tutor Details)
1st
Here. A tricky one.
Eric Nicholas K
Eric Nicholas K
4 months ago
I went in the wrong step by using double angle formula the first time. If you used that the first time, then you can try my current method.