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It is not just trial and error, as this will eat away time in the exam. if you can't see it straight away then you need to consider some things. for example a common question might be find the integral of...

to find the derivative, we can first make this easier to visualise. Say a second variable, y, is included to make this become y = arcsinx. now if we sin both sides, we get siny = x. we already know the de...

Using the question, first use de Moivre's theorem to say (cos x + i sin x)^5 = cos 5x + isin 5x. Now we can use a binomial expansion on the RHS to say 

cos 5x + isin 5x = cos⁵ x + 5i cos...