Question

cos 15 - sin 15 = 1 ÷√2

Answer 1

cos 15 can be written as
sin(90-teeta)
= sin(90-15)
=sin 75
so sin 75- sin 15 =sin 60
which is equal to 1/√2

Answer 2

Hello!

Here is your answer!!

To prove = cos 15° - sin 15° = 1 / √2

Left hand Side :

cos 15° - sin 15°

=> sin 75° - sin 15° ( As we know that cos 15 = cos ( 90 - 15 ) = sin 75

Now using the formula :

sin A - sin B

=>$= 2cos \frac{c + d}{2} sin \: \: \frac{c - d}{2}$

=>$= 2 \: cos \: \frac{75 + 15}{2} sin \: \frac{75 - 15}{2}$

=> 2 cos 45° sin 30°

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

=>$\frac{1}{ \sqrt{2} }$

Hope it helps u√