Question

what is the value of cosec 75​

Answer 1

Answer:

The answer is $\sqrt 6-\sqrt 2$

Step-by-step explanation:

$\cos ec75^\circ=\frac{1}{\sin 75^\circ}=\frac{1}{\sin(45^\circ+30^\circ)}$

             $=\frac{1}{\sin 45^\circ\cos30^\circ+\sin 30^\circ\cos45^\circ }\\=\frac{1}{\frac{1}{\sqrt 2}\times \frac{\sqrt 3}{2}+\frac{1}{2}\times \frac{1}{\sqrt 2}}\\=\frac{1}{\frac{\sqrt 3+1}{2\sqrt 2}}=\frac{2\sqrt 2}{\sqrt 3+1}\\=\frac{2\sqrt 2}{\sqrt 3+1}\times \frac{\sqrt 3-1}{\sqrt 3-1}\\=\frac{2\sqrt2(\sqrt 3-1)}{3-1}=\sqrt 2(\sqrt 3-1)=\sqrt 6-\sqrt 2$

Using $\sin (A+B)=\sin A\cos B+\cos A\sin B$