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Good Ramkumar!!
The technique used in this solution is called, method of universal substitution, x=tan (x/2) is the universal subtitution we are tallking abt. using this substitution, many complicated trignometric problems can be converted to algebraic problems. Once we express sinx and cosx in terms of tan (x/2), the whole expression turns to a an expression in tan (x/2). Which will be purely algebraic, once we put t=tan (x/2).
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