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Q.

What will be the expression of the following in terms of trigonometric ratio of angles lying between 0 °  and 45 °  , tan 80 ° +cot 70 °  ?


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a

cot 20 ° +tan 30 °  

b

cot 10 ° +tan 25 °  

c

cot 10 ° +tan 20 °  

d

cot 15 ° +tan 20 °   

answer is C.

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Detailed Solution

Given that tan 80 ° +cot 70 °  .
We use,
tan( 90 ° θ)=cotθ; cot( 90 ° θ)=tanθ  
We get,
=tan (9010) ° +cot (9020) °   =cot 10 ° +tan 20 °  
Thus the expression is cot 10 ° +tan 20 °  .
Therefore the correct option is 3.
 
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What will be the expression of the following in terms of trigonometric ratio of angles lying between 0 °  and 45 °  , tan 80 ° +cot 70 °  ?