Vær venlig at løse q 18?

I betragtning af det # A + B = 90 ^ @ # derefter # A = 90-B ^ @ #

#rarr (tanAtanB + tanAcotB) / (sinAsecB) - (sin ^ 2B) / (cos ^ 2A) #

# = (TANA tanB + cotB) / (sinAsecB) - (sin ^ 2B) / (cos ^ 2 (90 ^ @ - B) #

# = ((Annullere (sina) / cosa) sinB / cosB + cosB / sinB) / (annullere (sina) / cosB) - (sin ^ 2B) / (sin ^ 2B) #

# = ((1 / cosa) (sin ^ 2B + cos ^ 2B) / (sinB * annullere (cosB))) / (1 / annullere (cosB)) - 1 #

# = 1 / (cos (90 ^ @ - B) sinB) -1 #

# = 1 / sin ^ 2B-1 = (1-sin ^ 2B) / sin ^ 2B = (cos ^ 2B) / (sin ^ 2B) = cot ^ 2B #

I betragtning af det # A + B = 90 ^ @ # så er A = 90-B ^ @ #

Nu

# (TanAtanB + tanAcotB) / (sinAsecB) - (sin ^ 2B) / (cos ^ 2A) #

# (Tan (90 ^ @ - B) tanB + tan (90 ^ @ - B) cotB) / (sin (90 ^ @ - B) SecB) - (sin ^ 2B) / (cos ^ 2 (90 ^ @ - B)) #

# = (CotBtanB + cotBcotB) / (cosBsecB) - (sin ^ 2B) / (sin ^ 2B) #

# = 1 + barneseng ^ 2B-1 = barneseng ^ 2B #