쇼는 신분을 증명합니까? 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) ^ @)

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

참고 사항 # cos (360-A) ^ @ = cosA와 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 sin (60-20) / (2sin20cos20) #

# = 4 / sqrt3 sin40 / sin40 #

# = 4 / sqrt3 #