If #A+B=315^0#, then what is the value of #(1-tanA)(1-tanB)#?

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Answer 1 · 2018-01-24T07:21:44

# 2#.

#A+B=315^@=360^@-45^@#.

#:. tan(A+B)=tan(360^@-45^@)#.

#:. (tanA+tanB)/(1-tanAtanB)=-tan45^@=-1#.

#:. tanA+tanB=-1+tanAtanB, or, #

#tanA+tanB-tanAtanB=-1..................(ast)#.

Now, #"the reqd. value="(1-tanA)(1-tanB),#

#=1-tanA-tanB+tanAtanB#,

#=1-(tanA+tanB-tanAtanB)#,

#=1-(-1).................................................[because, (ast)]#,

#rArr" The Reqd. Value"=2#.