Question

Prove the following trigonometric identity:
2/ (√3 cos x + sin x) = sec(π/6 - x)

Answer 1

\[\dfrac{2}{\sqrt3 cos x+sin x}=sec(\pi/6 -x)\]
right?

Answer 2

Yes. I have no idea how to do that on this site, but yes

Answer 3

let go from the right hand side
\[sec (\pi/6-x)=\dfrac{1}{cos(\pi/6-x)}\]

Answer 4

Now, manipulate a little bit the denominator
cos (pi/6 -x) = cos (pi/6) cos x+ sin(pi/6) sinx
cos pi/6= sqrt3/2
sin pi/6 = 1/2
just plug on them in , simplify and you get the left hand side

Answer 5

*all not on

Answer 6

That looks about right. Thank you!