Question

cosec 15°+sec 15°=????

Answer 1

Answer:

$\csc 15^\circ+\sec 15^\circ=2\sqrt{6}$

Step-by-step explanation:

Given : Expression $\csc 15^\circ+\sec 15^\circ$

To find : Solve the expression ?

Solution :

$\csc 15^\circ+\sec 15^\circ$

$=\frac{1}{\sin15^\circ}+\frac{1}{\cos15^\circ}$

$=\frac{\cos15^\circ+\sin15^\circ}{\sin15^\circ\cos15^\circ}$

Multiply and divide by $\frac{1}{\sqrt{2}}$

$=\frac{\frac{1}{\sqrt{2}}\cos15^\circ+\frac{1}{\sqrt{2}}\sin15^\circ}{\frac{1}{\sqrt{2}}\sin15^\circ\cos15^\circ}$

$=\frac{\frac{1}{\sqrt{2}}\cos15^\circ+\frac{1}{\sqrt{2}}\sin15^\circ}{\frac{1}{\sqrt{2}}\sin15^\circ\cos15^\circ}$

In numerator we apply $\sin A\cos B+\cos A\sin B=\sin(A+B)$

In denominator we apply $2\sin A\cos A=\sin 2A$

$=\frac{\sin(45+15)}{\frac{1}{2\sqrt{2}}\sin30^\circ}$

$=\frac{2\sqrt{2}\sin(60)}{\sin30^\circ}$

$=\frac{2\sqrt{2}\times \frac{\sqrt3}{2}}{\frac{1}{2}}$

$=2\sqrt{6}$

Therefore, $\csc 15^\circ+\sec 15^\circ=2\sqrt{6}$

Answer 2

Answer:

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