Kung tanim alpha = x + 1 & tan bita = x-1 Pagkatapos ay hanapin kung ano ang 2cot (alpha-bita) =?

Kung tanim alpha = x + 1 & tan bita = x-1 Pagkatapos ay hanapin kung ano ang 2cot (alpha-bita) =?
Anonim

Sagot:

# rarr2cot (alpha-beta) = x ^ 2 #

Paliwanag:

Kung ganoon, # tanalpha = x + 1 at tanbeta = x-1 #.

# rarr2cot (alpha-beta) #

# 2 / (tan (alpha-beta)) = 2 / ((tanalpha-tanbeta) / (1 + tanalpha * tanbeta)) = 2 (1 tanalphatanbeta) / (tanalpha-tanbeta) #

# = 2 (1+ (x + 1) * (x-1)) / ((x + 1) - (x-1)) #

# = 2 (kanselahin (1) + x ^ 2cancel (-1)) / (kanselahin (x) + 1cancel (-x) +1 = 2 x ^ 2/2 = x ^ 2 #

Sagot:

# 2cot (alpha-beta) = x ^ 2 #

Paliwanag:

Meron kami # tanalpha = x + 1 # at # tanbeta = x-1 #

Bilang #tan (alpha-beta) = (tanalpha-tanbeta) / (1 + tanalphatanbeta) #

# 2cot (alpha-beta) = 2 / tan (alpha-beta) = 2 (1 tanalphatanbeta) / (tanalpha-tanbeta) #

= # 2 (1+ (x + 1) (x-1)) / (x + 1- (x-1)) #

= # 2 * (1 + x ^ 2-1) / (x + 1-x + 1) #

= # (2x ^ 2) / 2 = x ^ 2 #