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Question

If tanπ4+x+tanπ4-x=a then find the value of tan2π4+x+tan2π4-x.


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Solution

Calculate the value of the given expression :

Given,

tanπ4+x+tanπ4-x=a

tanπ4+x+tanπ4+x2=a2tan2π4+x+tan2π4-x+2tanπ4+xtanπ4-x=a2a+b2=a2+b2+2ab...(i)

Using tanA+B=tanA+tanB1-tanAtanB

tanπ4+x+π4-x=tanπ4+x+tanπ4-x1-tanπ4+xtanπ4-xtanπ2=tanπ4+x+tanπ4-x1-tanπ4+xtanπ4-x1-tanπ4+xtanπ4-x=0tanπ2=,=a0tanπ4+xtanπ4-x=1

Put value of tanπ4+xtanπ4-x back in (i).

tan2π4+x+tan2π4-x+2=a2tanπ4+xtanπ4-x=1tan2π4+x+tan2π4-x=a2-2

Hence, value of tan2π4+x+tan2π4-x is a2-2.


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