Question

If cosec Ø =
=
1/2 cotØ, then find sin Ø.

Answer 1

$\huge\bold{\color{aqua}{Solution :-}}$

$\bold{\blue{cosec\:Ø}\:=\:\green{\frac{1}{2}\:cot\:Ø}}$

$\bold{\blue{To \:find\:}\red{sin\:Ø}}$

$\quad\bold{cosec\:Ø\:=\:\frac{1}{2}\:cot\:Ø}$

$\Rightarrow\bold{\frac{1}{sin\:Ø}×\frac{1}{cot\:Ø}\:=\:\frac{1}{2}\qquad\qquad\therefore\orange{cosec\:A=\frac{1}{sin\:A}}}$

$\Rightarrow\bold{\frac{1}{sin\:Ø}×\frac{1}{\frac{cos\:Ø}{sin\:Ø}}\:=\:\frac{1}{2}\qquad\qquad\therefore\orange{cot\:A=\frac{cos\:A}{sin\:A}}}$

$\Rightarrow\bold{\frac{1}{sin\:Ø}×\frac{sin\:Ø}{cos\:Ø}\:=\:\frac{1}{2}}$

$\Rightarrow\bold{\frac{1}{\red{\cancel{\blue{sin\:Ø}}}}×\frac{\red{\cancel{\blue{sin\:Ø}}}}{cos\:Ø}\:=\:\frac{1}{2}}$

$\Rightarrow\bold{\frac{1}{cos\:Ø}\:=\:\frac{1}{2}}$

$\Rightarrow\bold{\green{\boxed{\red{cos\:Ø\:}=\pink{\:2}}}}$

$\bold{\purple{\text{Since the value of cos Ø can't be more than 1 but here we}}}$

$\bold{\purple{\text{are getting value of cos Ø = 2 which is greater than 1 }}}$

$\bold{\purple{\text{henceforth this question is wrong, we can't find real value}}}$

$\bold{\purple{\text{of sin Ø}}}$