Trigonometry> Sir pls solve this trigonometric eqn....

Sir pls solve this trigonometric eqn.

HEMANT , 10 Years ago

Grade 12

2 Answers

Sunil Raikwar

Last Activity: 10 Years ago

we can write given equation
sinx = -cosec²x/2
but we know that minimum value of cosec²ø is 1 & maximum value of sinøis 1
simultaneously this is not possible sinx=-1 & cosec²x/2=1, so given equation have no solution.

Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
We can rearange the given equation as:
$1+sinxsin^{2}\left ( \frac{x}{2} \right )=0\Rightarrow sinxsin^{2}\left ( \frac{x}{2} \right )=-1\Rightarrow sinx=-cosec^{2}\left ( \frac{x}{2} \right )$ This equation wouldnt have any solution as:
$for \quad x=\pi, \quad cosec^{2}\left ( \frac{x}{2} \right )=1; \quad sin(x)=0; for \quad x=\-pi, \quad cosec^{2}\left ( \frac{x}{2} \right )=-1; \quad sin(x)=0$
Since the function doesnt have a solution at the extremes and at the centre, we can assume that the function isnt defined throughout the interval and therefore it doesnt have a solution.
Regards
Sumit