Question

If sin A = 3/8, find the value of cosec A - sec A.​

Answer 1

`\csc A - \sec A = \frac 83 + (8)/(√(55))\\\\\csc A - \sec A = \frac 83 - (8)/(√(55))`

Step by step explanation:

`\text{Given that,}\\\\~~~~~~\sin A = \frac 38 \\\\\implies \sin^2 A = \frac 9{64}\\\\\implies 1 - \cos^2 A = (9)/(64)\\\\\implies \cos ^2 A = 1 - \frac 9{64}\\\\\implies \cos^2 A = (55)/(64)\\\\\implies \cos A =\pm\sqrt{(55)/(64)}\\ \\\implies \cos A = \pm\frac{√(55)}8\\\\`

`\implies \frac 1{\cos A} = \pm(8)/(√(55))`

`\text{Now,}\\\\\csc A - \sec A\\\\=(1)/(\sin A)- (1)/(\cos A)\\\\=\frac 83 -\left(\pm \frac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \frac 83 + (8)/(√(55))\\\\\csc A - \sec A = \frac 83 - (8)/(√(55))`