1.    If acos3Ɵ + 3acosƟsin2Ɵ = m, asin3Ɵ + 3acos2ƟsinƟ = n, prove that (m+n)2/3 + (m-n)2/3 = 2a2/3
asked May 23, 2013 in Trigonometry Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

2 Answers

answered Jan 11 by Mathical Level 10 User (55,420 points)

If this is an identity it has to be true for all a and theta.

Let ø=90 degrees, then m=0 and n=-a-3a=-4a.

Let ø=30 then m=9a/4 and n=7a/4. 

So in the first case we have to prove 0+4a*2/3=2a*2/3 which is clearly untrue. Even if 2/3 was an exponent, the two sides of the supposed equality are unequal. So instead of an identity it becomes an equation to be solved for theta.

In the second case we have 8a/3+a/3=3a≠2a(2/3).

The question needs to be corrected, perhaps to solve for theta.

The apparent appearance of the fraction 2/3 on each term suggests that it can be removed from the supposed identity (if it is a multiplier) in which case 2m=2a and m=a. This implies that a solution is theta=2nπ where n is an integer.

If 2/3 is an exponent the equation may be trickier to solve.

answered Jan 11 by Rod Top Rated User (442,220 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
78,519 questions
82,359 answers
63,330 users