Solve without the use of a calculator:

Question

sin20(tan10+cot10)

I know it should equal two but I don't know how to get there

Answer 1

sin20(tan10+cot10)
= sin20(sin10/cos10 + cos10/sin10)
= 2sin10cos10(sin^2 10 + cos^2 10)/(sin10cos10)
= 2(sin10cos10)/(sin10cos10 ( 1)
= 2