Question

# The value of tan $$130^o$$ tan $$140^o$$ is equal to

A
1
B
1
C
1/3
D
1+3

Solution

## The correct option is B $$1$$$$tan\left( 270 \right) =tan\left( 130+140 \right)$$ $$\Rightarrow tan\left( 180+90 \right) =\cfrac { tan\left( 130 \right) +tan\left( 140 \right) }{ 1-tan\left( 130 \right) .tan\left( 140 \right) }$$ $$\Rightarrow \cfrac { 1 }{ 0 } =\cfrac { tan\left( 130 \right) +tan\left( 140 \right) }{ 1-tan\left( 130 \right) .tan\left( 140 \right) }$$ $$\Rightarrow 1-tan\left( 130 \right) .tan\left( 140 \right) =0$$ $$\Rightarrow tan\left( 130 \right) .tan\left( 140 \right) =1$$Mathematics

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