Evaluate: \(\frac{sin30^o + tan45^o - cosec45^o}{sec30^o + cos60^0 +

1.	Evaluate: \(\frac{sin30^o + tan45^o - cosec45^o}{sec30^o + cos60^0 + cot45^o}\)
Answer» \(\frac {sin30° + tan 45° - cosec 45° }{sec30° + cos60° + cot 45°}\) \(= \cfrac {\frac12 + 1 - \sqrt2}{\frac2{\sqrt 3} + \frac 12 + 1}\) \(= \cfrac {\frac 32 - \sqrt 2}{\frac 32 + \frac 2{\sqrt3}}\) \(= \cfrac{\frac{3 - 2\sqrt 2}2}{\frac{3\sqrt 3 + 4} {2\sqrt 3}}\) \(= \frac {(3 - 2\sqrt 2) (3\sqrt 3 - 4)\sqrt 3}{(3\sqrt 3 + 4)(3\sqrt 3 - 4)}\) \(= \frac {(9\sqrt 3 - 6\sqrt 6 - 12 + 8\sqrt 2)\sqrt 3}{27 - 16}\) \(=\frac 1{11} (9\sqrt 3 - 6\sqrt 6 + 8\sqrt2 -12) \sqrt 3\)

Evaluate: \(\frac{sin30^o + tan45^o - cosec45^o}{sec30^o + cos60^0 + cot45^o}\)

Answer»

\(\frac {sin30° + tan 45° - cosec 45° }{sec30° + cos60° + cot 45°}\)

\(= \cfrac {\frac12 + 1 - \sqrt2}{\frac2{\sqrt 3} + \frac 12 + 1}\)

\(= \cfrac {\frac 32 - \sqrt 2}{\frac 32 + \frac 2{\sqrt3}}\)

\(= \cfrac{\frac{3 - 2\sqrt 2}2}{\frac{3\sqrt 3 + 4} {2\sqrt 3}}\)

\(= \frac {(3 - 2\sqrt 2) (3\sqrt 3 - 4)\sqrt 3}{(3\sqrt 3 + 4)(3\sqrt 3 - 4)}\)

\(= \frac {(9\sqrt 3 - 6\sqrt 6 - 12 + 8\sqrt 2)\sqrt 3}{27 - 16}\)

\(=\frac 1{11} (9\sqrt 3 - 6\sqrt 6 + 8\sqrt2 -12) \sqrt 3\)