Todista, että: -cot ^ -1 (theta) = cos ^ -1 (theta) / 1 + (theta) ²?

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

Päästää #cot ^ (- 1) theeta = A # sitten

# RarrcotA = theta #

# RarrtanA = 1 / theta #

# RarrcosA = 1 / SecA = 1 / sqrt (1 + tan ^ 2A) = 1 / sqrt (1 + (1 / theta) ^ 2) #

# RarrcosA = 1 / sqrt ((1 + theta ^ 2) / theeta ^ 2) = theta / sqrt (1 + theta ^ 2) #

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

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