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.

]]>Can you please explain something about that?]]>

I was breaking my head on this without getting the head or tail of the question.You made it so simple.

I got the answer and its right.

Thanks again. ]]>

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