Question

sin10 ori cos15 ori ctg10 ori tg170 / tg10 ori cos 165 ori ctg170 ori sin 190...VA ROG!​

Answer 1

$\dfrac{\sin\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(10\right)\cdot\tan\left(170\right)}{\tan\left(10\right)\cdot\cos\left(165\right)\cdot\cot\left(170\right)\cdot\sin\left(190\right)} = \\ \\ = \dfrac{\sin\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(10\right)\cdot\tan\left(180-10\right)}{\tan\left(10\right)\cdot\cos\left(180-15\right)\cdot\cot\left(180-10\right)\cdot\sin\left(180+10\right)} =$

$=\dfrac{\sin\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(10\right)\cdot\tan\left(-10\right)}{\tan\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(-10\right)\cdot\sin\left(10\right)} =$

$=\dfrac{-\sin\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(10\right)\cdot\tan\left(10\right)}{-\tan\left(10\right)\cdot\cos\left(15\right)\cdot\cot\left(10\right)\cdot\sin\left(10\right)} = \\ \\ = \boxed{1}$