(1+tanA*tanB)^2 +(tanA-tanB)^2=sec^2A*sec^2B ?

1 Answer
Jane
Feb 25, 2018

Given,

#( 1+ tan A tan B)^2 + (tan A - tan B)^2#

#= 1 +2 tan A tan B + tan ^2 A tan ^2 B + tan ^2 A - 2tan A tan B + tan ^2 B#

#= 1+ tan ^2 A + tan ^2 A tan ^2 B + tan ^2 B#

#= sec^2 A + tan ^2 B(tan ^2 A +1)# (as, #sec ^2 A -tan ^2 A =1#)

#= sec^2 A + tan^2 B* sec^2A#

# = sec ^2 A(1+ tan ^2 B)#

#= sec ^2 A sec ^2 B#

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