Günahı nasıl hesaplarsınız (cos ^ -1 (5/13) + tan ^ -1 (3/4))?

Cevap:

#sin (cos ^ (-1) (5/13) + tan ^ (- 1) (3/4)) = 63/65 #

Açıklama:

let #cos ^ (- 1) (5/13) = x # sonra

# Rarrcosx = 5/13 #

# Rarrsinx = sqrt (1 Cos ^ 2x) = sqrt (1- (5/13) ^ 2) 12/13 # =

# Rarrx = sin ^ (- 1) (12/13) = cos ^ (- 1) (5/13) #

Ayrıca, izin #tan ^ (- 1) (3/4) y # = sonra

# Rarrtany = 3/4 #

# Rarrsiny = 1 / cscy = 1 / sqrt (1 + yatağı ^ 2y) = 1 / sqrt (1 + (4/3) ^ 2) = 3/5 #

# Rarry = tan ^ (- 1) (3/4) = sin ^ (- 1) (3/5) #

#rarrcos ^ (- 1) (5/13) + tan ^ (- 1) (3/4) #

# = Sin ^ (- 1) (12/13) + sin ^ (- 1) (3/5) #

# = Sin ^ (- 1) (12/13 * sqrt (1- (3/5) ^ 2) + 3/5 * sqrt (1- (12/13) ^ 2)) #

# = Sin ^ (- 1) (12/13 * 4/5 + 3/5 * 5/13) = 63/65 #

Şimdi, #sin (cos ^ (- 1) (5/13) + tan ^ (- 1) (3/4)) #

# = Sin (sin ^ (- 1) (63/65)) = 63/65 #