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
secxcosx/secs=sin^2x
1tanxtany=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
 PreCalc  Trigonometric Identities Prove: (tanx + secx 1)/(tanx  secx + 1)= ...
 Trigonometry  Prove the following trigonometric identities. please give a ...
 Precalculus/Trig  I can't seem to prove these trig identities and would really ...
 Trigonometry.  ( tanx/1cotx )+ (cotx/1tanx)= (1+secxcscx) Good one! Generally...
 trig  express this in sinx (1/ cscx + cotx )+ (1/cscx cotx) i got 2sinx is ...
 Simplifying with Trigonometry Identities  Hi, I am a senior in High School ...
 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)/...
 Trigonometry Check  Simplify #3: [cosxsin(90x)sinx]/[cosxcos(180x)tanx] = [...
More Related Questions