Friday

October 31, 2014

October 31, 2014

Posted by **Joseph** on Thursday, December 9, 2010 at 6:45pm.

Verify.

csc^4x - cot^4x = 2csc^2x-1

- Precalculus -
**MathMate**, Friday, December 10, 2010 at 8:43amNot a surprise that you don't get it,

the two expressions are not equivalent!

Start from left:

csc^4(x)-cot^4(x)

Factor sin^4(x) as denominator:

=(1-cos^4(x))/sin^4(x)

Factor as difference of two squares

= (1 + cos²(x)) (1 - cos²(x)) / sin^4(x)

=(1 + cos²(x))sin²(x)/sin^4(x)

=(1+cos²(x))/sin²(x)

=(2cos²(x)+sin²(x))/sin²(x)

=2cos²(x)/sin²(x)+1

=2cot²(x)+1

(and not 2csc²(x)+1)

**Answer this Question**

**Related Questions**

Precalculus - Having trouble with this: Verify: csc^4x-cot^4x=2csc^2x-1 *the ...

trig - verify : [sec(x) / csc(x) - cot(x)] - [sec(x) / csc(x) + cot(x)] = 2csc(x...

trig - For each expression in column I, choose the expression from column II to ...

math (trig) - Prove: sin^2(x/2) = csc^2x - cot^2x / 2csc^2(x) + 2csc(x)cot(x) On...

Math - What is the first step. Explain please. Which expression is equivalent to...

pre cal - can someone please show me how to verify this identity? (sec x/csc x ...

Math - Trig - I'm trying to verify these trigonometric identities. 1. 1 / [sec(x...

precalculus - 1.csc^2x-1/csc^2x=cos^2x 2.1/1-cosx+1/1+cosx=2csc^2x 3.sinxcosy+...

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

Trigonometry - Hello all, In our math class, we are practicing the trigonometric...