Cos2x is an important identity in trigonometry which can be expressed in different ways. Cos 2x is one of the double angle trigonometric identities as the angle in consideration is a multiple of 2, that is, the double of x. Let us write the cos 2x identity in different forms: cos 2x = cos 2 x - sin 2 x. cos 2x = 2cos 2 x -. Freemath problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Detailedstep by step solution for cos(x)=sin(1/(2x)) This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. tanx y) = (tan x tan y) / (1 tan x tan y) . sin(2x) = 2 sin x cos x cos(2x) = cos ^2 (x) - sin ^2 (x) = 2 cos ^2 (x) - 1 = 1 - 2 sin ^2 (x) . tan(2x) = 2 tan(x) / (1 m2YJa. Purplemath In mathematics, an "identity" is an equation which is always true. These can be "trivially" true, like "x = x" or usefully true, such as the Pythagorean Theorem's "a2 + b2 = c2" for right triangles. There are loads of trigonometric identities, but the following are the ones you're most likely to see and use. Basic & Pythagorean, Angle-Sum & -Difference, Double-Angle, Half-Angle, Sum, Product Content Continues Below Need a custom math course?K12 College Test Prep Basic and Pythagorean Identities Notice how a "co-something" trig ratio is always the reciprocal of some "non-co" ratio. You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine. The following particularly the first of the three below are called "Pythagorean" identities. sin2t + cos2t = 1 tan2t + 1 = sec2t 1 + cot2t = csc2t Note that the three identities above all involve squaring and the number 1. You can see the Pythagorean-Thereom relationship clearly if you consider the unit circle, where the angle is t, the "opposite" side is sint = y, the "adjacent" side is cost = x, and the hypotenuse is 1. We have additional identities related to the functional status of the trig ratios sin−t = −sint cos−t = cost tan−t = −tant Notice in particular that sine and tangent are odd functions, being symmetric about the origin, while cosine is an even function, being symmetric about the y-axis. The fact that you can take the argument's "minus" sign outside for sine and tangent or eliminate it entirely for cosine can be helpful when working with complicated expressions. Angle-Sum and -Difference Identities sinα + β = sinα cosβ + cosα sinβ sinα − β = sinα cosβ − cosα sinβ cosα + β = cosα cosβ − sinα sinβ cosα − β = cosα cosβ + sinα sinβ By the way, in the above identities, the angles are denoted by Greek letters. The a-type letter, "α", is called "alpha", which is pronounced "AL-fuh". The b-type letter, "β", is called "beta", which is pronounced "BAY-tuh". Double-Angle Identities sin2x = 2 sinx cosx cos2x = cos2x − sin2x = 1 − 2 sin2x = 2 cos2x − 1 Half-Angle Identities The above identities can be re-stated by squaring each side and doubling all of the angle measures. The results are as follows Sum Identities Product Identities You will be using all of these identities, or nearly so, for proving other trig identities and for solving trig equations. However, if you're going on to study calculus, pay particular attention to the restated sine and cosine half-angle identities, because you'll be using them a lot in integral calculus. URL Subscribe to verify your answer Subscribe Sign in to save notes Sign in Show Steps Number Line Examples identity\\sin2x identity\\cos2x identity\\sin^2x+\cos^2x Description List trigonometric identities by request step-by-step trigonometric-identity-calculator identity \sin^2x+\cos^2x en Related Symbolab blog posts High School Math Solutions – Trigonometry Calculator, Trig Identities In a previous post, we talked about trig simplification. Trig identities are very similar to this concept. An identity... Read More Trigonometry Examples Popular Problems Trigonometry Simplify sin2x/sinx-cos2x/cosx Step 1Apply the sine double-angle 2Cancel the common factor of .Tap for more steps...Step the common by .Step 3Rewrite as a 4Write as a fraction with denominator .Step for more steps...Step by .Step from to .