Simplify ^@\dfrac{ 1 }{ 1 + sec \theta } + \dfrac {1} { 1 - sec | Maths Question and Answer | Edugain India

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Simplify $\dfrac{ 1 }{ 1 + sec \theta } + \dfrac {1} { 1 - sec \theta }$ .

Answer:

$-2 cot^2 \theta$

Step by Step Explanation:

Let,
$S =$ $\dfrac{ 1 }{ 1 + sec \theta } + \dfrac {1} { 1 - sec \theta }$
On adding two fractions,
$\begin{align} & \implies S = \dfrac { (1 - sec \theta) + (1 + sec \theta) } { (1 + sec \theta)(1 - sec \theta) } \\ & \implies S = \dfrac {2} { 1 - sec^2 \theta } \end{align}$
Using identity: $sec^2 \theta - 1 = tan^2 \theta,$
$\begin{align} & \implies S = \dfrac {2} { (-tan^2 \theta) } \\ & \implies S = -2 cot^2 \theta \end{align}$

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