How do you express $sin θ - csc θ + sec θ$ $sin theta - csc theta + sec theta$ in terms of $cos θ$ $cos theta$ ?

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Answer 1 · 2016-01-12T07:48:25

$= \frac{1 - {cos}^{3} (θ)}{cos (θ) \sqrt{1 - {cos}^{2} (θ)}}$ $=(1-cos^3(theta))/(cos(theta)sqrt(1-cos^2(theta))$

$sin (θ) - csc (θ) + sec (θ)$ $sin(theta) - csc(theta) + sec(theta)$

$= sin (θ) - \frac{1}{sin (θ)} + \frac{1}{cos (θ)}$ $=sin(theta)- 1/sin(theta) +1/cos(theta)$

$= \frac{sin (θ) sin (θ) - 1}{sin (θ)} + \frac{1}{cos (θ)}$ $=(sin(theta)sin(theta)-1)/sin(theta) + 1/cos(theta)$

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

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

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

$= (- {cos}^{2} (θ) \cdot cos (θ)) + \frac{1}{sin (θ) cos (θ)}$ $=(-cos^2(theta)*cos(theta))+1/(sin(theta)cos(theta))$

$= \frac{- {cos}^{3} (θ) + 1}{cos (θ) \sqrt{1 - {cos}^{2} (θ)}}$ $=(-cos^3(theta)+1)/(cos(theta)sqrt(1-cos^2(theta))$

$= \frac{1 - {cos}^{3} (θ)}{cos (θ) \sqrt{1 - {cos}^{2} (θ)}}$ $=(1-cos^3(theta))/(cos(theta)sqrt(1-cos^2(theta))$

How do you express sinθ−cscθ+secθsin theta - csc theta + sec theta in terms of cosθcos theta ?