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Question

If secA=x+14x then prove that secA+tanA=2xor12x

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Solution

Let,
secA+tanA=y ..............1
Then,
=sec2Atan2A=1
=(secAtanA)(secA+tanA)=1
=y(secAtanA)=1
=secAtanA=1y ....................2


Adding eq. 1 and eq. 2,we get
=2secA=y+1y
=2(x+14x)=y+1y
=2x+12x=y+1y
=y=2x or y=12x (on comparing two sides )
secA+tanA=2x ,12x


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