The number of solutions of equation esin x − 2e– sin x = 2 is

Take esinx = t (t > 0)⇒ t − 2 t = 2 <!- [if gte mso 9]><xml> </xml><! [endif]->⇒ <!- [if gte mso 9]><xml> </xml><! [endif]-> t 2 − 2 t = 2 ->t2 – 2t – 2 = 0->t2 – 2t + 1 = 3⇒ (t −1)2 = 3⇒ t = 1 ± 3 <!- [if gte mso 9]><xml> </xml><! [endif]->⇒ t = 1 ± 1.73⇒ t = 2.73 or –0.73 (rejected as t > 0)⇒ esin x = 2.73->loge esin x = loge 2.73⇒ sin x = loge 2.73 > 1So no solution.

The number of solutions of equation esin x − 2e– sin x = 2 is

More than 2

Ask & Answer Question

Maths NCERT Exemplar Solutions Class 11th Chapter Eight Ncert Solutions Maths class 12th Maths Class 12th

The number of solutions of equation e^{sin x} − 2e^{– sin x} = 2 is

Option 1 -

More than 2

Option 2 -

Option 3 -

Option 4 -

2 Views | Posted a week ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a week ago

Correct Option - 4

Detailed Solution:

Take e^sinx = t (t > 0)

⇒ $t - \frac{2}{t} = 2$

⇒ $\frac{t^{2} - 2}{t} = 2$

->t² – 2t – 2 = 0

->t² – 2t + 1 = 3

⇒ (t −1)² = 3

⇒ t = 1 ± $\sqrt[]{3}$

⇒ t = 1 ± 1.73

⇒ t = 2.73 or –0.73 (rejected as t > 0)

⇒ e^{sin x} = 2.73

->log_e e^{sin x} = log_e 2.73

⇒ sin x = log_e 2.73 > 1

So no solution.

Take esinx = t (t > 0)⇒ <math> <mrow> <mi>t</mi> <mo>−</mo> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820304315"> </o:OLEObject></xml><! [endif]->⇒ <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820304316"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mfrac> <mrow> <msup> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> </mrow> </math> ->t2 – 2t – 2 = 0->t2 – 2t + 1 = 3⇒   (t −1)2 = 3⇒   t = 1 ± <math> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820304317"> </o:OLEObject></xml><! [endif]->⇒   t = 1 ± 1.73⇒   t = 2.73 or –0.73 (rejected as t > 0)⇒   esin x = 2.73->loge esin x = loge 2.73⇒ sin x = loge 2.73 > 1So no solution.