Question

Упростите выражение ctgt+tg(-t)/cost+sin(-t)+tg(-t)/sint

Answer 1

$dfrac{ctgt+tg(-t)}{cost+sin(-t)}+ dfrac{tg(-t)}{sint} = \ \ = dfrac{ frac{cost}{sint}- frac{sint}{cost} }{cost-sint}- dfrac{ frac{sint}{cost} }{sint} = \ \ = dfrac{ frac{cos^2t-sin^2t}{sintcost} }{cost-sint}- dfrac{1}{cost} = \ \ = dfrac{cos^2t-sin^2t}{sintcost(cost-sint)} - dfrac{1}{cost}= \ \ = dfrac{(cost-sint)(cost+sint)}{sintcost(cost-sint)}- dfrac{1}{cost}= \ \ = dfrac{cost+sint-sint}{sintcost}= \ \ = dfrac{cost}{sintcost}= \ \ = dfrac{1}{sint}$