Ipakita ang patunayan ang pagkakakilanlan sa ibaba? 1 / cos290 + 1 / (sqrt3sin250) = 4 / sqrt3

# LHS = 1 / (cos290 ^ @) + 1 / (sqrt3sin250 ^ @) #

# = 1 / (cos (360-70) ^ @) + 1 / (sqrt3sin (180 + 70) ^ @) #

# = 1 / (cos70 ^ @) - 1 / (sqrt3sin70 ^ @) #

# = (sqrt3sin70 ^ @ - cos70 ^ @) / (sqrt3sin70 ^ @ cos70 ^ @) #

# = 1 / sqrt3 (2 {sqrt3sin70 ^ @ - cos70 ^ @}) / (2sin70 ^ @ cos70 ^ @) #

# = 1 / sqrt3 (2 * 2 {sin70 ^ @ * (sqrt3 / 2) -cos70 ^ @ * (1/2)}) / (sin140 ^ @) #

# = 1 / sqrt3 (4 {sin70 ^ @ * cos30 ^ @ - cos70 ^ @ * sin30 ^ @}) / (sin (180-40) ^ @) #

# = 1 / sqrt3 (4 {sin (70-30) ^ @}) / (sin40 ^ @) = 1 / sqrt3 (4 {cancel (sin40 ^) = 4 / sqrt3 = RHS #

TANDAAN iyon #cos (360-A) ^ @ = cosA at sin (180 + A) ^ @ = - sinA #

# 1 / cos290 + 1 / (sqrt3sin250) #

# = 1 / cos (270 + 20) + 1 / (sqrt3sin (270-20)) #

# = 1 / sin20 - 1 / (sqrt3cos20) #

# = (sqrt3cos20-sin20) / (sqrt3sin20cos20) #

# = 2 / sqrt3 (sqrt3 / 2cos20-1 / 2sin20) / (sin20cos20) #

# = 4 / sqrt3 (sin60cos20-cos60sin20) / (2sin20cos20) #

# = 4 / sqrt3 kasalanan (60-20) / (2sin20cos20) #

# = 4 / sqrt3 sin40 / sin40 #

# = 4 / sqrt3 #

Ipakita na ang kayumanggi (52.5 °) = sqrt6 - sqrt3 - sqrt2 + 2?

(1 + (1 / sqrt (3))) / (1- (1 / sqrt (3)) = ( sqrt (3) +1) / (sqrt (3) -1) = 2 + sqrt (3) rarrtan52.5 = cot (90-37.5) = cot37.5 rarrcot37.5 = 1 / (tan (75/2) (x / 2)) rarrtanx = (2tan (x / 2)) / (1-tan ^ 2 (x / 2)) rarrtanx-tanx * tan ^ 2 (X / 2) -tanx = 0 Ito ay parisukat sa kayumanggi (x / 2) Kaya, rarrtan (x / 2) = (- 2 + sqrt (2 ^ 2-4 * tanx * (- tanx (X 2) = (- 2 + sqrt (4 (1 + tan ^ 2x))) / (2 * tanx) rarrtan (x / 2) = (- 1 + sqrt (1 + tan ^ 2x)) / tanx Ang paglalagay ng x = 75 makakakuha tayo ng rarrtan (75/2) = (- 1 + sqrt (1 + tanong ^ 2 (75))) / (tan75) rarrtan (75/2) (2 + sqrt (3)) ^ 2)) / (2 + sqrt (3)) rarrtan

Ano ang sqrt {-sqrt3 + sqrt (3 + 8 sqrt (7 + 4 sqrt3?

Kung ang isa ay maaaring gumamit ng isang calculator, ang 2 Kung walang calculator ay pinapayagan, pagkatapos ay dapat maglaro sa paligid sa mga batas ng surds at gumamit ng algebraic manipulation upang gawing simple ito. Pumunta sa ganitong paraan: sqrt (7 + 4sqrt (3)) = sqrt (4 + 2 * 2sqrt (3) +3) = sqrt (2 ^ 2 + 2 * 2sqrt (3) + sqrt3 ^ 2) = sqrt ((2 (sqrt3) ^ 2) = 2 + sqrt3 {Ito ay gumagamit ng pagkakakilanlan (a + b) ^ 2 = a ^ 2 + b ^ 2 + 2ab} sqrt (3 + 8sqrt (7 + 4sqrt3) 8 * (2 + sqrt3) = sqrt (3 + 16 + 8sqrt3) = sqrt (16 + 2 * 4sqrt3 + 3) = sqrt ((4 + sqrt3) ^ 2) = 4 + sqrt3 { sqrt (-sqrt3 + sqrt (3 + 8sqrt (7 + 4sqr

Isulat ang kumplikadong numero (sqrt3 + i) / (sqrt3-i) sa karaniwang form?

(sqrt 3 + i) / (sqrt3 - i) Multiply at hatiin sa pamamagitan ng (sqrt3 + i) sa pamamagitan ng rationalizing ang denamineytor, => (sqrt3 + i) ^ 2 / ((sqrt3-i) * (sqrt3 + i)) => (sqrt3 + i) ^ 2 / (3 + 1) kulay (indigo) (=> ((sqrt3 + ) / 2) ^ 2