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Question

If sin[2cos1cot(2tan1x)]=0, then the value of x=



Correct Answer
A

±(1±2)
 

Your Answer
B

±(12)
 

Your Answer
C

(1+2)
 

Your Answer
D

(21)


Solution

The correct option is B

±(1±2)
 


Given sin[2cos1cot(2tan1x)]
sin{2cos1[cot(tan12x1x2)]}=0sin{2cos1[cot(cot11x22x)]}=0sin{2cos1(1x22x)}=0             [2cos1z=cos1(2z21)]2cos1(1x22x)=cos1[2(1x22x)21]=cos1[x44x2+12x2]LHS=sin[cos1(x44x2+12x2)]           .........(1)Again sin(cos1t)=sin(sin11t2)=01t2=0Hence from (1) (x44x2+1)2(2x2)2=0[(x44x2+12x2)] [(x44x2+1+2x2)]=0x44x2+1+2x2=0              x44x2+12x2=0(x21)2=0             (x23)2=8x=±1              x=±(1±2)

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