A-Math - Trigonometry - Trigonometric Identities (5) (3-6cos^2 x)/(sinx-cosx)=3(sinx+cosx)

A-Math - Trigonometry - Trigonometric Identities (5)

$\frac{{3 - 6{{\cos }^2}x}}{{\sin x - \cos x}} = 3(\sin x + \cos x)$

$A-Math - Trigonometry - Trigonometric Identities (5) (3-6cos^2 x)/(sinx-cosx)=3(sinx+cosx)$

Topic: Trigonometry

We will start manipulating from the side that looks more complicated,
in this case,it is the left hand side (LHS). If you look at the question, you
realize that

$3 - 6{\cos ^2}x$ looks somewhat similar to the double angle
formula

$2{\cos ^2}x - 1 = \cos 2x$ and we can change the numerator

$2{\cos ^2}x - 1 = \cos 2x = {\sin ^2}x - {\cos ^2}x$ to cancel out

$\sin x - \cos x$ in the denominator.

If you practice enough question on proving trigonometric identities, you
will be able to look at the question and come up with a plan to manipulate
rather quickly, it is from experience and EXPERIENCE=PRACTICE.

Additional Math (A-Maths) and Math (E-Math) Tutor in Woodlands, Chua Chu Kang,
Sembawang, Bukit Panjang, Yishun and Johor Bahru.

About Unknown

I created this Blog after my students told me that there is very little information about how to solve GCE O Level Math and Additional Math (A-Math) questions on the internet. Even if they manage to find, the solution were for very basic questions. I am a Full-time Math Tutor in Singapore. I tutor mainly in Northern Singapore (Woodlands, Chua Chu Kang, Bukit Panjang, Yishun and Sembawang). I also tutor in Johor Bahru.