Question

Question #41efc

Answer 1

Prove trig identity

Explanation:

Left side of the equation:
`sin t/(1 - cos t)`
Right side of the equation.
`RS = csc t + cot t = 1/(sin t) + cos t/(sin t) = (1 + cos t)/(sin t) (1)`
Multiply the left side, both numerator and denominator, with (1 + cos t)
`LS = ((sin t)(1 + cos t))/((1 - cos t)(1 + cos t)) = ((sint)(1 + cos t))/(1 - cos^2 t) =`
`= (sint (1 + cos t))/sin^2 t = (1 + cos t)/(sin t) (2)`

Compare (1) and (2), we get LS = RS