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Question

Assertion :If a>b>0 & ac<1<bc, then tan1(ab1+ab)+tan1(bc1+bc)+tan1(ca1+ac)=π Reason: tan1xtan1y=tan1(xy1+xy)x,y

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion false but Reason is true
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Solution

The correct option is C Assertion is correct but Reason is incorrect
tan1xtan1y
⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪tan1(xy1+xy) if xy>1π+tan1(xy1+xy) if x>0,y<0,xy<1π+tan1(xy1+xy) if x<0,y>0,xy<1
Now a>b>0 so ab>0
tan1(ab1+ab)=tan1atan1b .....( i )
And bc>1
tan1(bc1+bc)=tan1btan1c......( ii )
Also ac<1 & a>0,c<0
tan1(ca1+ca)=π+tan1ctan1a.....( iii )
On adding (i), (ii) & (iii) we get
tan1(ab1+ab)+tan1(bc1+bc)+tan1(ca1+ca)
Assertion (A) is correct
By fact Reason is false

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