Question

prove that sin 105 degree + cos 105 degree equal to one by root 2

Answer 1

we can write sin 105 to sin75.
and also cos 105 to (-cos75).
now, value of sin75 is root 3 +1/2 root2

Answer 2

to solve this we have to convert given values in standard form

so, sin 105° = sin 60°+ sin45°

and cos 105° = sin 60° + sin 45°

therefore,

sin 60 + sin 45 + cos 60 + cos 45

=
$\sqrt{3} \div 2 + 1 \div \sqrt{2} + 1 \div 2 + 1 \div \sqrt{2}$
solving this u get result as
$1 \div \sqrt{2}$