How do you verify the identity $tan (θ + \frac{π}{2}) = - cot θ$ $tan(theta+pi/2)=-cottheta$ ?

Question

How do you verify the identity $tan (θ + \frac{π}{2}) = - cot θ$ $tan(theta+pi/2)=-cottheta$ ?

1 Answer

Impact of this question

10288 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-16T11:33:18

$see explanation$ $"see explanation"$

Explanation:

$using the addition formulae for sin/cos$ $"using the "color(blue)"addition formulae for sin/cos"$

$∙ x sin (x + y) = sin x cos y + cos x sin y$ $•color(white)(x)sin(x+y)=sinxcosy+cosxsiny$

$∙ x cos (x + y) = cos x cos y - sin x sin y$ $•color(white)(x)cos(x+y)=cosxcosy-sinxsiny$

$tan (θ + \frac{π}{2}) = \frac{sin (θ + \frac{π}{2})}{cos (θ + \frac{π}{2})}$ $tan(theta+pi/2)=(sin(theta+pi/2))/(cos(theta+pi/2))$

$sin (θ + \frac{π}{2}) = sin θ cos (\frac{π}{2}) + cos θ sin (\frac{π}{2})$ $sin(theta+pi/2)=sinthetacos(pi/2)+costhetasin(pi/2)$

$\times \times \times \times = sin θ (0) + cos θ (1) = cos θ$ $color(white)(xxxxxxxx)=sintheta(0)+costheta(1)=costheta$

$cos (θ + \frac{π}{2}) = cos θ cos (\frac{π}{2}) - sin θ sin (\frac{π}{2})$ $cos(theta+pi/2)=costhetacos(pi/2)-sinthetasin(pi/2)$

$\times \times \times \times = cos θ (0) - sin θ (1) = - sin θ$ $color(white)(xxxxxxxx)=costheta(0)-sintheta(1)=-sintheta$

$tan (θ + \frac{π}{2}) = \frac{cos θ}{- sin θ} = - cot θ as required$ $tan(theta+pi/2)=costheta/(-sintheta)=-cottheta" as required"$

Science

Math

Humanities

... and beyond

How do you verify the identity $tan (θ + \frac{π}{2}) = - cot θ$ $tan(theta+pi/2)=-cottheta$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you verify the identity tan(θ+π2)=−cotθtan(theta+pi/2)=-cottheta?

1 Answer

Explanation:

Related questions

Impact of this question

How do you verify the identity $tan (θ + \frac{π}{2}) = - cot θ$ $tan(theta+pi/2)=-cottheta$ ?