pls help me with all the question
1. let * be the binary operation defined by a*b = ab .a,b belongs to N .is * associative
2. evaluate tan-1 [ 2 cos ( 2 sin-1 1/2 )]
3. WRITE THE PRINCIPAL VALUE OF cos-1 (cos 2 pie /3) + sin -1(sin 2 pie /3)
4. PROVE THAT tan( pie/4 + cos-1 a/b) + tan ( pie/4 - cos-1 a/b) = 2b/a
5. SOLVE FOR x cos-1 ( x2 - 1/x2 +1) + tan-1 (2x/ x2 - 1) = 2pie/3
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