How do you simplify the expression $\frac{{sec}^{2} θ - 1}{{sec}^{2} θ}$ $(sec^2theta-1)/sec^2theta$ ?

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How do you simplify the expression $\frac{{sec}^{2} θ - 1}{{sec}^{2} θ}$ $(sec^2theta-1)/sec^2theta$ ?

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Answer 1 · 2016-10-30T21:39:59

$\Rightarrow \frac{\frac{1}{{cos}^{2} θ} - 1}{\frac{1}{{cos}^{2} θ}}$ $=>(1/cos^2theta - 1)/(1/cos^2theta)$

$\Rightarrow \frac{\frac{1}{{cos}^{2} θ} - \frac{{cos}^{2} θ}{{cos}^{2} θ}}{\frac{1}{{cos}^{2} θ}}$ $=> (1/cos^2theta - cos^2theta/cos^2theta)/(1/cos^2theta)$

$\Rightarrow \frac{\frac{1 - {cos}^{2} θ}{{cos}^{2} θ}}{\frac{1}{{cos}^{2} θ}}$ $=>((1 - cos^2theta)/cos^2theta)/(1/cos^2theta)$

We use the identity ${sin}^{2} β + {cos}^{2} β = 1 \to {sin}^{2} β = 1 - {cos}^{2} β$ $sin^2beta + cos^2beta = 1-> sin^2beta = 1 - cos^2beta$ .

$\Rightarrow \frac{{sin}^{2} θ}{{cos}^{2} θ} \times \frac{{cos}^{2} θ}{1}$ $=>(sin^2theta)/cos^2theta xx cos^2theta/1$

$\Rightarrow {sin}^{2} θ$ $=>sin^2theta$

Hopefully this helps!

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How do you simplify the expression $\frac{{sec}^{2} θ - 1}{{sec}^{2} θ}$ $(sec^2theta-1)/sec^2theta$ ?

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