Choose the correct option and justify your choice:
$fraction numerator 1 minus tan squared 45 degree over denominator 1 plus tan squared 45 degree end fraction$

(A) tan 90° (B) 1 (C) sin 45° (D) 0.

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Solution

fraction numerator 1 minus tan squared 45 degree over denominator 1 plus tan squared 45 degree end fraction space equals space fraction numerator 1 minus left parenthesis 1 right parenthesis squared over denominator 1 plus left parenthesis 1 right parenthesis squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 minus 1 over denominator 1 plus 1 end fraction equals 0 over 2 equals 0

∴ Ans. (D).

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