Confirming Trigonometric Equation Solutions

[sarah786]

i have solved some questions but my answers don't match with the solution list i have in my book... please if you help me check my answers, i'll be very grateful..

√3 tan x - sec x - 1 = 0 ... i get three solutions to this question but my book's got two... it doesn't mention 5pi/3 + 2n*pi... do u think this is also a soln to this question??

sin2x + sin x = 0 ... one of the solutions that i get is 4pi/3 + 2n*pi ... my book doesn't mention this... am i correct??

sin 4x - sin 2x = cos 3x ... one of the solutions that i get is pi/2 + 2n*pi/3 ... am i right?

sin x + sin 3x + sin 5x = 0 ... are pi/3 + 2n*pi and 2n*pi/3 also solutions to this eq. ??

LAST ONE :) ... sin θ + sin 3θ + sin 5θ + sin 7θ = 0 ... is 3*pi/4 + n*pi also a solution...

I really need to confirm the answers i am having my grand test tomorrow... i have tried them but not sure about the answers... i will be grateful forever if you confirm these... thanks :)

 

[Mark44]

i have solved some questions but my answers don't match with the solution list i have in my book... please if you help me check my answers, i'll be very grateful..

√3 tan x - sec x - 1 = 0 ... i get three solutions to this question but my book's got two... it doesn't mention 5pi/3 + 2n*pi... do u think this is also a soln to this question??

5pi/3 + 2n*pi is not a solution. This is easy enough to check, using pi/3 for the reference angle. tan(pi/3) = √3, sec(pi/3) = 2, so tan(5pi/3) = -√3 and sec(5pi/3) = 2. Substituting into your equation gives
√3(-√3) - 2 - 1 = -3 - 2 - 1 = -6.

For the rest of your problems you should check them yourself. You've already done the hardest work. Checking your solutions involves determining whether you get a true statement when you replace the variable in the equation by the value you're checking.

sin2x + sin x = 0 ... one of the solutions that i get is 4pi/3 + 2n*pi ... my book doesn't mention this... am i correct??

sin 4x - sin 2x = cos 3x ... one of the solutions that i get is pi/2 + 2n*pi/3 ... am i right?

sin x + sin 3x + sin 5x = 0 ... are pi/3 + 2n*pi and 2n*pi/3 also solutions to this eq. ??

LAST ONE :) ... sin θ + sin 3θ + sin 5θ + sin 7θ = 0 ... is 3*pi/4 + n*pi also a solution...

I really need to confirm the answers i am having my grand test tomorrow... i have tried them but not sure about the answers... i will be grateful forever if you confirm these... thanks :)