Question

cos(a-b)=cos Acos B+SinAsinB
find the value of
1) cos 15
2) sin 75

Answer 1

cos15=cos(60-45)
=cos60.cos45-sin60.sin45
$1 \div 2 \times 1 \ \sqrt{2} - \sqrt{3} \div 2 \times 1 \div \sqrt{2}$
$1 \div 2 \sqrt{2} - \sqrt{3} \div 2 \sqrt{2}$
$1 - \sqrt{3 } \div 2 \sqrt{2}$
$cos15 = 1 - \sqrt{3} \div 2 \sqrt{2}$
sin75= sin(45+30)
=sin45.cos30+cos45.sin30

$sin75 = 1 \div \sqrt{2} \times \sqrt{3} \div 2 + 1 \div \sqrt{2} \\ \sqrt{2} \times 1 \div 2$
$sin75 = \sqrt{3} + 1 \div 2 \sqrt{2}$
i hope this help u.
thanks