Trigonometry IdentitiesDate: 07/30/97 at 14:14:18 From: luis manuel lozano Subject: Trigonometry identities have a problem with these identities. I don't know the answer - please help me: 1. 1-tanA + secA = 1+tanA ------ ---- -------- secA tanA secAtanA 2. tanA - senA = secA+cosA ----- ---- --------- cscA - cotA cscA+cotA 3. tanA+sec3A-secA = tan2A+senA --------------- secA 4. cosA+senAcotA = 2 senA ------------- cotA 5. senX = 1+cosX ------ ------ 1-cosX senX 6. sen2X = cosX+1 ------ ------ secX-1 secX 7. csc4Y-1 = csc2Y+1 ------- cot2Y 8. 1-3senY - 4sen2Y = 1-4senY ----------------- -------- cos2Y 1-senY Thank you very much. Date: 08/01/97 at 13:52:12 From: Doctor Rob Subject: Re: Trigonometry identities One technique that works very well in these examples is to express everything in sight in terms of sin(A) and cos(A) (or X or Y instead of A). Another simplifying thing to do is to clear all fractions by multiplying both sides of the equation by the least common multiple of all its denominators. For example, I'll work through number 1 for you, and you do the rest: 1 - tan(A) + sec(A) = 1 + tan(A) ---------- ------ ------------- sec(A) tan(A) sec(A)*tan(A) Clear fractions by multiplying by sec(A)*tan(A): tan(A) - tan^2(A) + sec^2(A) = 1 + tan(A). Subtract tan(A) from both sides: -tan^2(A) + sec^2(A) = 1. Write in terms of sine and cosine: -(sin(A)/cos(A))^2 + (1/cos(A))^2 = 1. Clear fractions again by multiplying by cos^2(A): -sin^2(A) + 1 = cos^2(A). This should look familiar to you! Add sin^2(A) to both sides: 1 = sin^2(A) + cos^2(A). This is one of the fundamental identities, so you are done. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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