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Cevap:

# (Tan315tan30) / (+ tan315tan30 1) = - (2 + SQRT (3)) #

Açıklama:

#rarr (tan315tan30) / (+ tan315tan30 1) #

# = Kahve renkli (315-30) #

# = Tan285 #

# = Kahve renkli (+15 270) #

# = - cot15 #

# = - 1 / tan15 #

# = - 1 / tan (45-30) #

# = - 1 / ((tan45tan30) + tan45tan30 / (1)) #

# = (Tan30 + 1) / (tan30-1) #

# = (1 / SQRT3 + 1) / (/ sqrt3-1 1) #

# = (1 + sqrt (3)) / (1-sqrt (3)) #

# = (1 + sqrt (3)) ^ 2 / (- 2) = - (2 + sqrt (3)) #

Cevap:

# -2-sqrt (3) #

Açıklama:

Biz biliyoruz ki, #tan (A-B) = (tanAtanB) / (1 + tanAtanB) #

Yani, # (Tan315 ^ 0tan30 ^ 0) / (1 + tan315 ^ 0tan30 ^ 0) = tan (315 ^ 0-30 ^ 0) = tan285 ^ 0 = tan (^ 0 360 ^ 0-75) = - tan75 ^ 0 = 2-SQRT3 #

VEYA

# Tan315 ^ 0 = tan (270 ^ 0 + ^ 0 45) = - tan45 ^ 0 = -1andtan30 ^ 0 = 1 / SQRT3 #

yani, # (Tan315 ^ 0tan30 ^ 0) / (1 + tan315 ^ 0tan30 ^ 0) = (- 1-1 / SQRT3) / (1-1 * / SQRT3 1) #

# = - ((sqrt (3) 1) / (sqrt (3) 1)) * ((sqrt (3) 1) / (sqrt (3) -1) =) - (3 + 2sqrt (3) + 1) / (3-1) = - (4 + 2sqrt3) / 2 = -2-SQRT3 #