The general solution of the equation tan2(x+y)+cot2(x+y)=1ā2xāx2 lie on the line is :
A
x=−1
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B
x=−2
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C
y=−1
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D
y=−2
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Solution
The correct option is Ax=−1 tan2(x+y)+cot2(x+y)=1−2x−x2tan2(x+y)+cot2(x+y)=−[x2+2x+1]+2≤2tan2(x+y)+cot2(x+y)=2−(x+1)2ForsolutiontoexistRHS=LHS(x+1)2=0⇒x=−1Hence,optionAiscorrectanswer.