Buktikan bahawa: -cot ^ -1 (theta) = cos ^ -1 (theta) / 1 + (theta) ²?

Buktikan bahawa: -cot ^ -1 (theta) = cos ^ -1 (theta) / 1 + (theta) ²?
Anonim

Biarkan #cot ^ (- 1) theta = A # kemudian

# 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) / theta ^ 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))) #