first rationalise it

get the num.(root(2) + root(1+cosx)/1-cosx

now write 27^x as 3^3x

and  9^x=3^2x

take 3^2x common from both of them u will get

(3^x-1)(3^2x-1) (root(2) + root(1+cosx)/2sin^2 x/2

now multiply and divide by 2x^2 .

it will become [log3. log3]  (apply property - lim x->0 (a^x-1/x)=loga)

and then limsinx/x=1

u will get answer