# Trig

prove the identity

(sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2

sinX^6= sinx^2 ^3 = (1-cosX^2)^3
= (1-2CosX^2 + cos^4) (1-cosX^2)
then multiply that out
1-2CosX^2 + cos^4 - cosX^2 + 2cos^4 -cos^6

add that on the left to the cos^6, and combine terms..
1-3CosX^2 + 3cos^4
1-3cos^2x (i-cos^2 x)

then use the sin^2 x=1-cos^2 x and you have it.

1. 👍 0
2. 👎 0
3. 👁 157

## Similar Questions

1. ### Trig........

I need to prove that the following is true. Thanks (cosx / 1-sinx ) = ( 1+sinx / cosx ) I recall this question causing all kinds of problems when I was still teaching. it requires a little "trick" L.S. =cosx/(1-sinx) multiply top

asked by abdo on April 18, 2007
2. ### Pre-calc

prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i need steps to show how i got the answer generally, it is a good idea to change all trig ratios to sines and cosines, and start with the more complicated-looking

asked by Stacey on May 6, 2007
3. ### Trigonometry Check

Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [cosx-(sin90cosx-cos90sinx)sinx]/[cosx-(cos180cosx+sinx180sinx)tanx] = [cosx-((1)cosx-(0)sinx)sinx]/[cosx-((-1)cosx+(0)sinx)tanx] = [cosx-cosxsinx]/[cosx+cosxtanx] =

asked by Anonymous on February 20, 2012
4. ### Pre-Calc

Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 -

asked by Dave on January 2, 2007
5. ### trigonometry

can i use factoring to simplify this trig identity? the problem is sinx + cotx * cosx i know the answer is cscx and i know how to get it but i want to know if i can do factoring to get it bc i tried to but it wont give me the

asked by v on December 3, 2012
6. ### math

tanx+secx=2cosx (sinx/cosx)+ (1/cosx)=2cosx (sinx+1)/cosx =2cosx multiplying both sides by cosx sinx + 1 =2cos^2x sinx+1 = 2(1-sin^2x) 2sin^2x + sinx-1=0 (2sinx+1)(sinx-1)=0 x=30 x=270 but if i plug 270 back into the original

asked by shan on September 6, 2008
7. ### Math - Pre- Clac

Prove that each of these equations is an identity. A) (1 + sinx + cos x)/(1 + sinx + cosx)=(1 + cosx)/sinx B) (1 + sinx + cosx)/(1 - sinx + cosx)= (1 + sin x)/cosx Please and thankyou!

asked by Jonathan on December 14, 2009
8. ### Trigonometry.

( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! Generally these are done by changing everything to sines and cosines, unless you see some obvious identities. Also generally, it is best to start with the more complicated

asked by mo on April 18, 2007
9. ### Simplifying with Trigonometry Identities

Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each

asked by amanda on March 7, 2007
10. ### maths - trigonometry

I've asked about this same question before, and someone gave me the way to finish, which I understand to some extent. I need help figuring out what they did in the second step though. How they got to the third step from the

asked by anonymous on June 19, 2010

More Similar Questions