What is ${cot}^{2} θ - sec θ$ $cot^2theta-sectheta$ in terms of $sin θ$ $sintheta$ ?

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Answer 1 · 2018-06-17T15:17:35

$(\frac{1 - {sin}^{2} θ}{{sin}^{2} θ}) - (\frac{1}{\sqrt{1 - {sin}^{2} θ}})$ $((1-sin^2theta)/(sin^2theta))-((1)/sqrt(1-sin^2theta))$

The identities used in this question are

$1)$ $1)$ ${cos}^{2} θ + {sin}^{2} θ = 1$ $cos^2theta+sin^2theta=1$

$2)$ $2)$ ${cot}^{2} θ = \frac{{cos}^{2} θ}{{sin}^{2} θ}$ $cot^2theta=(cos^2theta)/(sin^2theta)$

$3)$ $3)$ $sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

So

$\Rightarrow {cot}^{2} θ - {sec}^{2} θ$ $=>cot^2theta-sec^2theta$

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

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

What is cot^2theta-sectheta cot2θ−secθcot^2theta-sectheta in terms of sinthetasinθsintheta?