Mind you I recommend that you first understand the standard method like what Bob did. Once you do you can experiment with other methods.
Also, it is not a shortcut, it requires that you learn more mathematics. But in case you get stuck an alternative method is always good.
]]>Oh, that looks evil. But what can you do? Just use trig. formulas as they present themselves.
(i) Write sec as 1/cos and cosec as 1/sin
(ii) Put over common denominator.
(iii) Throw in some 2s to make root 3 into sin(x) and 1 into cos(x) and to get an extra factor of 2 on the denominator. Where you introduce a /2 or x2, compensate by x2 or /2 as necessary. Leave any additional 2s alone.
(iv) Use sin(2y) = 2sin(y).cos(y) on the denominator and sin(x-y) = sin(x).cos(y) - sin(y).cos(x) on the numerator.
(v) Simplify.
(vi) Look smug when all that is left is the answer. (What! no 'smug' smiley? I'll just have to make do with these.)
Bob
]]>options are:-
A) 4.5
B) 4
C) 8
D) 9