Use the properties of the trigonometric functions to find the exact value, without using a calculator

Question

1+2csc(-145 degrees) sin(35 degrees)

Answer 1

csc(-145°) = csc(-145° + 360°) = csc215° = csc(35° + 180°) = 1 / [sin(35° + 180°) = -1/sin35°

So, 1 + 2csc(-145°)sin35° = 1 - 2 = -1