How do you express $tan θ - {cot}^{2} θ$ $tan theta - cot^2theta$ in terms of $cos θ$ $cos theta$ ?

Question

How do you express $tan θ - {cot}^{2} θ$ $tan theta - cot^2theta$ in terms of $cos θ$ $cos theta$ ?

1 Answer

Impact of this question

3054 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-16T06:21:13

Explanation is given below.

Explanation:

$tan θ - {cot}^{2} θ$ $tantheta - cot^2theta$

On handiling these kind of problem apply your previous knowledge on identity.

$tan θ = \frac{sin θ}{cos θ}$ $tantheta = sintheta/costheta$

$cot θ = \frac{cos θ}{sin θ}$ $cottheta = costheta/sintheta$

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

Our problem:

$tan θ - {cot}^{2} θ$ $tantheta - cot^2theta$

$= \frac{sin θ}{cos θ} - \frac{{cos}^{2} θ}{{sin}^{2} θ}$ $=sintheta/costheta - cos^2theta/sin^2theta$

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

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

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

Science

Math

Humanities

... and beyond

How do you express $tan θ - {cot}^{2} θ$ $tan theta - cot^2theta$ in terms of $cos θ$ $cos theta$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express tanθ−cot2θtan theta - cot^2theta in terms of cosθcos theta ?

1 Answer

Explanation:

Related questions

Impact of this question

How do you express $tan θ - {cot}^{2} θ$ $tan theta - cot^2theta$ in terms of $cos θ$ $cos theta$ ?