How do you verify the identity $(cot^2x-1)/(1+cot^2x)=1-2sin^2x$ ?

Question

How do you verify the identity $(cot^2x-1)/(1+cot^2x)=1-2sin^2x$ ?

1 Answer

Impact of this question

16153 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-05T12:10:17

see explanation.

Explanation:

We attempt to express the left side in the same form as the right side.
Let's begin by rewriting $cot^2x$

$color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(cotx=(cosx)/(sinx))color(white)(a/a)|)))$

$rArr((cos^2x)/(sin^2x)-1)/(1+cos^2x/(sin^2x)$

now multiply all terms on numerator and denominator by $sin^2x$

$rArr(cos^2x-sin^2x)/(sin^2x+cos^2x) .......(A)$

To simplify we require the $color(blue)"trigonometric identities"$

$color(orange)"Reminder"$

$color(red)(|bar(ul(color(white)(a/a)color(black)(cos2x=cos^2x-sin^2x=1-2sin^2x)color(white)(a/a)|)))$

and $color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2x+cos^2x=1)color(white)(a/a)|)))$

Substituting these into (A) gives.

$cos2x=1-2sin^2x$

Thus left side = right side $rArr" verified"$

Science

Math

Humanities

... and beyond

How do you verify the identity $(cot^2x-1)/(1+cot^2x)=1-2sin^2x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you verify the identity (cot^2x-1)/(1+cot^2x)=1-2sin^2x(cot^2x-1)/(1+cot^2x)=1-2sin^2x?

1 Answer

Explanation:

Related questions

Impact of this question

How do you verify the identity $(cot^2x-1)/(1+cot^2x)=1-2sin^2x$ ?