Identifying trigonometric identities?
104581
It takes practice!  And its like a puzzle.  Just use the main trig identities as reference and a good math tutor.  Unfortunately, this place isn't the best place to ask that kind of question because we are limited by text explainations and trig identities need a lot more than that!
880627
Do you mean verifying trig identities?\n\nTry: ask dr math\n\nIf you have a specific trig question, write back.\n\nGuido
756840
cosx=tanx\ncosx=sinx/cosx\ncos^2(x)=sinx\n1-sin^2(x)=sinx    {pythagoras}\nsin^2(x)+sinx-1=0\nuse quadratic formula\nsinx=(-1+or-sqrt(5))/2\n=0.6180339888\nor -1.6180339888\nsine has to lie between +/-1\nsinx= 0.6180339888\nx=arcsin(0.6180339888)\n  =38.17270763\n+ve value for sine lies in 1st and 2nd\nquadrants \ntherefore,x=38.17270763 degrees or\n141.8272924 degrees\n\nthese two values were checked in the \noriginal equation and were found \nto be correct\n\ni hope that this helps
938105
learn your identities well and as far as possible reduce all ratios to basic ratios of sine and cosine
932480
sin(A+B)sin(A-B)/(cos²Acos²B)\n= (sinAcosB + cosAsinB)(sinAcosB - cosAsinB)/(cos²Acos²B)\n= (sin²Acos²B - cos²Asin²B)/(cos²Acos²B) (since (x + y)(x - y) = x² - y²)\n= sin²A/cos²A - sin²B/cos²B\n= tan²A - tan²B ← Option c)\n\nPlease note: sin(A + B) = sinAcosB + cosAsinB\nand sin(A - B) = sinAcosB - cosAsinB
95376
SOHCAHTOA....geometry term Sine Opposite Over Hypotenuse,Cosine adjacent over hypotenuse, Tangent opposite Over Adjacent
105824
Trigonometry.  The good old days when I still loved math... ahhh!
484958
sin 2x=2 sinx . cos x\ncos 2x=(cos x)^2-(sin x)^2\ncos 2x=2 (cos x)^2 -1\ncos 2x=1- 2 (sin x)^2\ntan 2x=(sin 2x)/(cos 2x)\n\nor you can \nsin 2x=1\nlet 2x=y\nsin y=1\ny=90 degree + 360 degree\n2x=90 degree + 360 degree\nx=45 degree + 180 degree\nso x={45,225,....}degree\n\ntan x+cot x=2/sin 2x:\ntan x+cot x\n=(sin x/cos x )+(cos x/sin x)\n=((sin x)^2+(cos x)^2)/(sin x . cos x)\n=1/(sin x . cos x)\n=2/2(sin x . cos x)\n=2/sin 2x\nso it is an identity
27697
There is a use for the logic you need to solve them.*That answer came from my trig. teacher, and I have no idea, I failed my identities test.*
623185
Kind of sounds like Chinese Trigonometry to me! Is this a question or an answer???
1150095
its sooo easy  \nsinA-sinB = 2 sin[(A-B)/2] * cos[(A-B)/2]\ncosA - cosB = 2 cos[(A-B)/2] * cos[(A-B)/2]\nthus LHS = \n(2 sin[(A-B)/2] * cos[(A-B)/2]) / (2 cos[(A-B)/2] * cos[(A-B)/2])\n= sin[(A-B)/2] / cos[(A-B)/2]\n= tan[(A-B)/2 \n= tan (A/2-B/2)\n=RHS \n\nhence proved
610758
sin(2x) = 2sinxcosx is a trigonometric identity called the double angle identity. It was derived from another identity:\n\n   sin(x + y) = sinxcosy + cosxsiny\n \nhere x and y are two different angles but what if x = y\nreplace y with x to make all the equations in terms of x, thus the equation becomes:\n\n   sin(x + x) = sinxcosx + cosxsinx\n   \nnote that sinxcosx is also equal to cosxsinx, so simplifying the equation it becomes:\n\n  sin(2x) = 2sinxcosx or sin(2x) = 2cosxsinx
879956
2 - csc²z =\n2 - (1/sin²z) = \n(2sin²z - 1) / sin²z = \n(sin²z + sin²z - 1 ) / sin²z =\n(sin²z - cos²z) / sin²z =  {using trig id sin²+cos²=1}\n1 - (cos²z / sin²z) =\n1 - cot²z\n\n~ ~ ~ ~\n\ncot³t / csct =\n(cos³t/sin³t) / (1/sint) =\n(cos³t/sin³t) * sint =\ncos³t/sin²t =\ncost (cos²t/sin²t) =\ncost (cot²t) = \ncost (csc² -1)  {using trig id 1+cot²=csc²}\n\nHope that helped!\n\n~ ♥ ~
319082
RHS cot a - tan b \n= cos a/sina - sinb/cosb \n= cosacosb - sinasinb/sinacosb\n= cos(a+b)/sinacosb\n= LHS (proven)\n\nThe idea is to prove that both sides are the same.
874407
sec x - 1 = tan x\nsec x = tan x + 1\nsec ^2 x = tan^2 x + 2 tan x + 1\n\n[Pythagorean identity: sin^2 x + cos^2 x = 1\nDivide through by cos^2 x to get tan^2 x + 1 = sec^2 x]\n\n(tan^2 x + 1) = tan^2 x + 2 tan x + 1\n2 tan x = 0\n\ntan x = 0 where sin x = 0, which is at x = 0, 180, or 360.
40284
(1) Subtitute the damn values for what you have.\n\n(2) Sin theta=opp/hyps,\n    Tan   "  =opp/adj,\n    Cos   "  =adj/hyps.\n\nNow usually a blind man follows his stick now you might know where you are at the moment - get it???
140502
The trigonometric identities have as their primary purpose to simplify calculations.  For example, why evaluate 2sinxcosx when you can evaluate sin2x.\n\nAs for the applications, oblique triangles are used in surveying and mapping.  For example, suppose you want to know your distance from an object on the opposite side of a river.  You can mark off a line of a fixed distance, say 100ft.  Then, go to the opposite ends of the line and use a transit to measure the angle between the object and the line you measured.  You can now determine all three sides with this information.