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Question

If sin [cot1(x+1)]=cos (tan1x), then find x.

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Solution

sin[cot1[1+x]]=cos[tan1x]
Now
cot1(1+x)=p & tan1x=9
cotp=1+x tanq=x
sinp=1(1+x)2+1 sinq=x1+x2;cosq=11+x2
then
sin[sin11(1+x)2+1]=cos[cos111+x2]
1(1+x)2+1=11+x1
squaring both side we get
1+x2=(1+x)2+x
x2=1+x2+2x
2x=-1
[x=12]

1212979_1365852_ans_56bb26dcef4040239acc822f79b783cd.JPG

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