Question #7bd62

Question

Question #7bd62

1 Answer

Related questions

How do you use the fundamental trigonometric identities to determine the simplified form of the...
How do you apply the fundamental identities to values of $θ$ $theta$ and show that they are true?
How do you use the fundamental identities to prove other identities?
What are even and odd functions?
Is sine, cosine, tangent functions odd or even?
How do you simplify $sec x cos (\frac{π}{2} - x)$ $sec xcos (frac{\pi}{2} - x )$ ?
If $csc z = \frac{17}{8}$ $csc z = \frac{17}{8}$ and $cos z = - \frac{15}{17}$ $cos z= - \frac{15}{17}$ , then how do you find $cot z$ $cot z$ ?
How do you simplify $\frac{{sin}^{4} θ - {cos}^{4} θ}{{sin}^{2} θ - {cos}^{2} θ}$ $\frac{\sin^4 \theta - \cos^4 \theta}{\sin^2 \theta - \cos^2 \theta}$ using...
How do you prove that tangent is an odd function?
How do you prove that $sec (\frac{π}{3}) tan (\frac{π}{3}) = 2 \sqrt{3}$ $sec(pi/3)tan(pi/3)=2sqrt(3)$ ?

Impact of this question

1503 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-03T13:24:23

$({tan}^{2} x) ({csc}^{2} x - 1) = ({tan}^{2} x) ((1 + {cot}^{2} x) - 1) = {tan}^{2} x {cot}^{2} x = 1$ $(tan^2x )(csc^2x -1) =(tan^2x)((1+cot^2x)-1) =tan^2xcot^2x=1$

Explanation:

The basic "Pythagoras" trig relationship is:
${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$ , from which you get the other two by dividing both sides either by ${sin}^{2} x$ $sin^2x$ or ${cos}^{2} x$ $cos^2x$ :
$1 + {cot}^{2} x = {csc}^{2} x$ $1+cot^2x=csc^2x$ and ${tan}^{2} x + 1 = {sec}^{2} x$ $tan^2x+1=sec^2x$ .

Remember that by definition $cot x = \frac{1}{tan x}$ $cotx=1/tanx$ , $sec x = \frac{1}{cos x}$ $secx=1/cosx$ and $csc x = \frac{1}{sin x}$ $csc x=1/sinx$ .

Science

Math

Humanities

... and beyond

Question #7bd62

1 Answer

Explanation:

Related questions

Impact of this question