Prokázat, že: -cot ^ -1 (theta) = cos ^ -1 (theta) / 1 + (theta) ²?

Prokázat, že: -cot ^ -1 (theta) = cos ^ -1 (theta) / 1 + (theta) ²?
Anonim

Nechat #cot ^ (- 1) theta = A # pak

# rarrcotA = theta #

# rarrtanA = 1 / theta #

# rarrcosA = 1 / secA = 1 / sqrt (1 + tan ^ 2A) = 1 / sqrt (1+ (1 / theta) ^ 2) # 2

# rarrcosA = 1 / sqrt ((1 + theta ^ 2) / theta ^ 2) = theta / sqrt (1 + theta ^ 2) #

# rarrA = cos ^ (- 1) (theta / (sqrt (1 + theta ^ 2))) = postýlka ^ (- 1) (theta) #

#rarrthereforecot ^ (- 1) (theta) = cos ^ (- 1) (theta / (sqrt (1 + theta ^ 2))) # #