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Learn how to derive and use the sin 2x formula in terms of sin, cos, and tan. Also, find the formulas of sin^2x in terms of cos and cos^2 using trigonometric identities.
- Double Angle Formula
Let us see the applications of the double angle formulas in...
- Period
According to the definition of a period of a function, a...
- Derivative of Sin 2x
To find the derivative of f(x) = sin 2x by the product rule,...
- Tangent Function
tan x = sin x/cos x; tan x = Opposite Side/Adjacent Side =...
- Integration
Integration is finding the antiderivative of a function. It...
- Double Angle Formula
In mathematics, an "identity" is an equation which is always true, regardless of the specific value of a given variable. An identity can be "trivially" true, such as the equation x=x or an identity can be usefully true, such as the Pythagorean Theorem's a2+ b2= c2. Content Continues Below.
The identity of cos2x helps in representing the cosine of a compound angle 2x in terms of sine and cosine trigonometric functions, in terms of cosine function only, in terms of sine function only, and in terms of tangent function only.
How do you use the fundamental identities to prove other identities? Divide the fundamental identity # sin^2x + cos^2x = 1# by #sin^2x# or #cos^2x# to derive the other two: #sin^2x/sin^2x + cos^2x/sin^2x = 1/sin^2x#. #1 + cot^2x = csc^2x#. #sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x#. #tan^2x + 1 = sec^2x#.
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 - tan ^2 (x))
30 lip 2017 · This can be rewritten two different ways: $$\sin^2 x = 1- \cos^2 x$$. and. $$\cos^2 x = 1 - \sin^2 x$$. Use either of these formulas to replace the $\sin^2 x$, or the $\cos^2 x$, on the right side of your identity. That will give you the other two forms. Share.
Free trigonometric identity calculator - verify trigonometric identities step-by-step
