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Question

If sinθ1sinθ2cosθ1cosθ21=0, where θ1+θ2(0,2π), then the value of (1+tanθ14)(1+tanθ24) is  


Solution

sinθ1sinθ2cosθ1cosθ2=1
cos(θ1+θ2)=1
θ1+θ2=π as θ1+θ2(0,2π) 
θ1+θ24=π4
θ24=π4θ14

(1+tanθ14)(1+tanθ24)
=(1+tanθ14)[1+tan(π4θ14)]
=(1+tanθ14)⎢ ⎢ ⎢21+tanθ14⎥ ⎥ ⎥=2 

Mathematics

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