Some Applications of Trigonometry

Choose the correct option and justify your choice: (A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°. - Wired Faculty

Question

Choose the correct option and justify your choice:
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(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°.

Solution

space space fraction numerator 2 tan 30 degree over denominator 1 plus tan squared 30 degree end fraction space equals space fraction numerator 2 cross times begin display style fraction numerator 1 over denominator square root of 3 end fraction end style over denominator 1 plus open parentheses begin display style fraction numerator 1 over denominator square root of 3 end fraction end style close parentheses squared end fraction space equals fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator 1 plus begin display style 1 third end style 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 space space equals space fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style 4 over 3 end style end fraction space equals space fraction numerator square root of 3 over denominator 2 end fraction space equals space sin space 60 degree

Ans. (A)