How do you verify the identify $cos θ csc θ tan θ = 1$ $costhetacscthetatantheta=1$ ?

Question

How do you verify the identify $cos θ csc θ tan θ = 1$ $costhetacscthetatantheta=1$ ?

1 Answer

Impact of this question

1926 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-02T15:11:16

Please see below.

Explanation:

All trigonometric ratios can be easily expressed in terms of $sin θ$ $sintheta$ and $cos θ$ $costheta$ .

For example, $tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$ , $cot θ = \frac{cos θ}{sin θ}$ $cottheta=costheta/sintheta$ , $sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$ and $csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$

Hence, $cos θ csc θ tan θ$ $costhetacscthetatantheta$

= $cos θ \times \frac{1}{sin θ} \times \frac{sin θ}{cos θ}$ $costhetaxx1/sinthetaxxsintheta/costheta$

= $color(red)(cancel(costheta))xx1/cancel(sintheta)xxcancel(sintheta)/color(red)(cancel(costheta))$

= $1$

Science

Math

Humanities

... and beyond

How do you verify the identify $cos θ csc θ tan θ = 1$ $costhetacscthetatantheta=1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you verify the identify costhetacscthetatantheta=1cosθcscθtanθ=1costhetacscthetatantheta=1?

1 Answer

Explanation:

Related questions

Impact of this question

How do you verify the identify $cos θ csc θ tan θ = 1$ $costhetacscthetatantheta=1$ ?