Question

Compute without using a calculator. 2 sin 765◦ + tan 1485◦ cot 135◦

Answer 1

765° = 45°
1485° = 45°

We get 2sin(45°) + tan(45°) + cot(135)

sin(45) = sqrt(2)/2
tan(45) = 1
cot(135) = -1

we get
2*[sqrt(2)/2)] + (1) + (-1)

= sqrt(2)

Answer 2

$2sin765^o+tan1485^ocot135^o\\\\=2sin(2\cdot360^o+45^o)+tan(8\cdot180^o+45^o)cot(90^o+45^o)\\\\=2sin45^o+tan45^o\cdot(-tg45^o)\\\\=2\cdot\frac{\sqrt2}{2}+1\cdot(-1)=\sqrt2-1$