What is $5 cos θ - 8 sec θ$ $5costheta-8sectheta$ in terms of $sin θ$ $sintheta$ ?

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Answer 1 · 2018-04-12T18:20:44

$5 cos θ - \frac{8}{cos (θ)}$ $5costheta - 8/cos(theta)$

$\frac{cos θ}{cos θ} \times \frac{5 cos θ}{1} - \frac{8}{cos θ}$ $costheta/costheta xx (5costheta)/1 - 8/costheta$

$\frac{5 {cos}^{2} θ}{cos θ} - \frac{8}{cos θ}$ $(5cos^2theta)/costheta- 8/costheta$

$\frac{5 {cos}^{2} θ - 8}{cos θ}$ $(5cos^2theta-8)/costheta$

${cos}^{2} θ = 1 - {sin}^{2} θ$ $cos^2theta = 1-sin^2theta$

$\frac{5 (1 - {sin}^{2} θ) - 8}{cos θ}$ $(5(1-sin^2theta)-8)/costheta$

$\frac{5 - 5 {sin}^{2} θ - 8}{cos θ}$ $(5-5sin^2theta - 8)/costheta$

$\frac{- 3 - 5 {sin}^{2} θ}{cos θ}$ $(-3-5sin^2theta)/costheta$

What is 5cosθ−8secθ5costheta-8sectheta in terms of sinθsintheta?