Question

If secA + tanA = x then secA =

Answer 1

if secA + tanA = x then $secA = \frac{x^{2}+1 }{2x}$

Given,

secA + tanA = x

To Find,

secA = ?

Solution,

To find secA,

Let us consider

secA + tanA = x  -----> eq 1

From the identity,

$sec^{2}A- tan^{2} A = 1$,

(secA+tanA) (secA-tanA) = 1

secA-tanA = 1/ secA-tanA

substituting from eq 1,

secA-tanA = 1/ x -----> eq 2

Adding eq 1 and 2,

we get,

2secA =x + 1/x

$2secA = \frac{x^{2}+1 }{x} \\secA = \frac{x^{2}+1 }{2x}$

Therefore if secA + tanA = x then $secA = \frac{x^{2}+1 }{2x}$

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Answer 2

if secA + tanA = x then \begin{gathered}secA = \frac{x^{2}+1 }{2x} \\\end{gathered}

secA=

2x

x

2

+1

Given,

secA + tanA = x

To Find,

secA = ?

Solution,

To find secA,

Let us consider

secA + tanA = x -----> eq 1

From the identity,

\begin{gathered}sec^{2}A- tan^{2} A = 1\\\end{gathered}

sec

2

A−tan

2

A=1

,

(secA+tanA) (secA-tanA) = 1

secA-tanA = 1/ secA-tanA

substituting from eq 1,

secA-tanA = 1/ x -----> eq 2

Adding eq 1 and 2,

we get,

2secA =x + 1/x

\begin{gathered}2secA = \frac{x^{2}+1 }{x} \\secA = \frac{x^{2}+1 }{2x} \\\end{gathered}

2secA=

x

x

2

+1

secA=

2x

x

2

+1

Therefore if secA + tanA = x then \begin{gathered}secA = \frac{x^{2}+1 }{2x} \\\end{gathered}

secA=

2x

x

2

+1