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Sir pls solve this trigonometric eqn.

Sir pls solve this trigonometric eqn.

Question Image
Grade:12

2 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 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 IIT Delhi
askIITians Faculty 137 Points
6 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

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