Question

Use the even-odd and periodic properties of the trigonometric functions to simplify.

a) csc(t) - 4 csc(-t)

b) -2 sin(3t + 2) - 3 sin(-3t)

Answer 1

The answer is given below

a) coseclt) – 4 Cogeeft). Since cosec is an odd function, so - Cosedt) = cosedt) This Coseelt) - 4 Cosech-t) = cosect) - 4€ Cosect)) closedt) + y cosect) = 5 cosecht) cosect). u caseelt) = 5 coser st) (6) – 2sin (3+ + 2*) —3 sink 3+) Using odd property of sin function sint-st) =- sintot)

Thus, And by periodic property sinlt +2A) = sint > Sinist+27) - Sinßt) -2sin (3t+22)-3sin(-3t) =-2 singt)-3(-sinßt)) c-2sinßt) + 3sinßt). = sin(t) - 28102t +22)-3sint3t) = sin(at)