Posted by **Jill** on Tuesday, January 14, 2014 at 11:10pm.

Which of the following are trigonometric identities?

(Can be more then one answer)

tanx cosx cscx = 1

secx-cosx/secs=sin^2x

1-tanxtany=cos(x+y)/cosxcosy

4cosx sinx = 2cosx + 1 - 2sinx

Find all solutions to the equation cosx cos(3x) - sinx sin(3x) = 0 on the interval [0,2π]. (Points : 5)

π/8,3π/8,5π/8,7π/8,9π/8,11π/8,13π/8,15π/8

π/8,5π/8,9π/8,13π/8

3π/8,7π/8,11π/8,15π/8

π/8,9π/8, 15π/8

- Math, please help -
**Reiny**, Wednesday, January 15, 2014 at 12:03am
tanx cosx cscx

= sinx/cosx * cosx * 1/sinx

= 1

so the first one is an identity

For questions like this, I use this trick

pick a weird angle, e.g x = 13.79°

If that weird angle satisfies your equation, it is "highly likely" that it is an identify.

( I know that it does not prove it, but I would put a large sum of money on it)

2nd one works

3rd works

4th does not

cosx cos(3x) - sinx sin(3x0 = 0

You should recognize that pattern and get

cos(x+3x) = 0

cos (4x) = 0

4x = π/2 or 4x = 3π/2

x = π/8 or x = 3π/8

now the period of cos (4x) = 2π/4 or π/2

so by adding multiples of π/2 to any answer will give up new answers

π/8

π/8 + π/2 = 5π/8

5π/8 + π/2 = 9π/8

9π/8 + π/2 = 13π/8

etc. (numerator jumping by 4π)

same for 3π/8 , adding π/2 yields more answers

3π/8 , 7π/8, 11π/8 , 15π/8 , next one would be > 2π

looks like you answer #1, with 8 different answers.

## Answer This Question

## Related Questions

- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- Trigonometry - Prove the following trigonometric identities. please give a ...
- Simplifying with Trigonometry Identities - Hi, I am a senior in High School ...
- trig - express this in sinx (1/ cscx + cotx )+ (1/cscx- cotx) i got 2sinx is ...
- Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...
- Math 12 - Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/sinx+...
- Math - Im really struggling with these proving identities problems can somebody ...
- Trigonometry - Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/...
- math - tanx+secx=2cosx (sinx/cosx)+ (1/cosx)=2cosx (sinx+1)/cosx =2cosx ...

More Related Questions