Math, asked by akshayaabhigna, 5 months ago

A+B=45 then prove (1+tanA) (1+tanB)=2

Answers

Answered by Anonymous

0

Answer:

Step-by-step explanation:

466

Answered by VivekPremi

0

Step-by-step explanation:

(1+tanA)(1+tanB)=x

1 + tanB + tanA + tanAtanB=x

(subtract both side by 2)

tanA + tanB -1+ tanAtanB=x-2

(divide both side by 1-tanAtanB)

{(tanA+tanB)/1-tanAtanB} - {(1-tanAranB)/(1-tanAtanB)}=

x-2/1-tanAtanB

tan(A+B) - 1 = x-2/1-tanAtanB

tan45 -1 = x-2/1-tanAtanB

0= x-2/1-tanAtanB [ tan45=1]

therefore,

x-2=0

x=2

since (1+tanA)(1+tanB)=x

therefore,

(1+tanA)(1+tanB)=2

hence proved

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