Thursday

August 28, 2014

August 28, 2014

Posted by **Timothy** on Monday, February 25, 2008 at 7:36pm.

In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; 1=1). I am not having much trouble with these problems, but two are proving rather difficult for me. They are:

csc^2(x)/cot(x)=csc(x)sec(x)

and

cot^3(x)/csc(x)=cos(x)*csc^2(x)-1

Could I please get a kick in the right direction?

Thanks,

Timothy

- Trigonometry -
**Christiaan**, Monday, February 25, 2008 at 8:21pm1)

cscē(x)=1/sinē(x) and cot(x)=cos(x)/sin(x)

=> cscē(x)/cot(x) = sin(x)/(sinē(x)*cos(x))

We can scrap one of the sinus factors in both the numerator and denominator, so that the expression equals:

1/(sin(x)*cos(x))

Since csc(x)=1/sin(x) and sec(x)=1/cos(x)

the expression we found equals csc(x)*sec(x). So we have proven the equality.

- Trigonometry -
**Christiaan**, Monday, February 25, 2008 at 8:23pm2)

csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x)

=> cot^3(x)/csc(x)=cos^3(x)*sin(x)/sin^3(x)

=cos^3(x)/sinē(x)

Now, we know that cosē(x)=1-sinē(x)

=> cos^3(x)=cos(x)*(1-sinē(x))=cos(x)-cos(x)*sinē(x)

So, when we fill this in in the equation we get that:

cos^3(x)/sinē(x)=(cos(x)-cos(x)*sinē(x))/sinē(x)

We can split this fraction in two seperate fractions, namely:

(cos(x)/sinē(x)) - (cos(x)*sinē(x)/sinē(x))

= cos(x)*cscē(x) - cos(x)

= cos(x) (cscē(x)-1)

It seems to me you forget a pair of brackets in your question.

- Trigonometry -
**Timothy**, Monday, February 25, 2008 at 8:44pmThank you very much for the assistance. I understand this perfectly. Have a good day. :)

**Related Questions**

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

algebra - Can someone please help me do this problem? That would be great! ...

Math - State the restrictions on the variables for these trigonometric ...

verifying trigonometric identities - How do I do these problems? Verify the ...

tigonometry - expres the following as sums and differences of sines or cosines ...

Trigonometry - Identities and proof - Show that cot((x+y)/2) = - (sin x - sin y...

Trigonometry - Proofs - Prove that the average of the numbers n sin (n degrees...

Trigonometry - Please review and tell me if i did something wrong. Find the ...

trig - it says to verify the following identity, working only on one side: cotx+...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...