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Question

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


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