1.

What is the value of \(\frac{{\cos 2{\rm{A\;}} + {\rm{\;}}2{{\cos }^2}{\rm{A\;}} - {\rm{\;}}2\cos 2{\rm{A}}\cos {\rm{A}}}}{{\sin 2{\rm{A\;}} - {\rm{\;}}2{{\sin }^2}{\rm{A}}\sin 2{\rm{A}}}}?\)1). (8 - 2√3) / √32). (2 + √3) / √33). (2√3 - 2) / √34). (2 - 2√3) / √3

Answer»

$(\frac{{\COS 2{\rm{A\;}} + {\rm{\;}}2{{\cos }^2}{\rm{A\;}} - {\rm{\;}}2\cos 2{\rm{A}}\cos {\rm{A}}}}{{\sin 2{\rm{A\;}} - {\rm{\;}}2{{\sin }^2}{\rm{A}}\sin 2{\rm{A}}}})$

PUT A = 30°

$(\Rightarrow \frac{{\cos 60{\rm{\;}} + {\rm{\;}}2{{\cos }^2}30 - {\rm{\;}}2\cos 60\cos 30}}{{\sin 60{\rm{\;}} - {\rm{\;}}2{{\sin }^2}30\sin 60}})$

$(\Rightarrow \frac{{\frac{1}{2}{\rm{\;}} + {\rm{\;}}2{\rm{\;}} \times {\rm{\;}}\frac{3}{4}\; - {\rm{\;}}2{\rm{\;}} \times {\rm{\;}}\frac{{\sqrt 3 }}{2}\; \times {\rm{\;}}\frac{1}{2}{\rm{\;}}}}{{\frac{{\sqrt 3 }}{2}{\rm{\;}} - {\rm{\;}}2 \times {\rm{\;}}\frac{1}{4}\; \times {\rm{\;}}\frac{{\sqrt 3 }}{2}}})$

⇒ (2 - √3/2) / (√3/2 - √3/4) = (8 - 2√3) /√3


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