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2. Fundamental Identities - Trigonometry - Socratic

   socratic.org/trigonometry/trigonometric-identities-and-equations/fundamental...

   Divide the fundamental identity # sin^2x + cos^2x = 1# by #sin^2x# or #cos^2x# to derive the other two:

3. Double Angle Identities - Trigonometry - Socratic

   socratic.org/trigonometry/trigonometric-identities-and-equations/double-angle...

   How do you verify #cos 2x = (1-tan^2x)/(1+tan^2x)# using the double angle identity? How do you use find the exact value of cos2x, given that cotx = -5/3 with pi/2<x<pi? How do you use a double-angle formula to find the exact value of cos2u when sin u = 7/25, where pi/2 <u < pi?

4. Proving Identities - Trigonometry - Socratic

   socratic.org/trigonometry/trigonometric-identities-and-equations/proving...

   How do you verify the identity #cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x#?

5. Cos 2X Identity, Graphing & Formula - Lesson | Study.com

   study.com/academy/lesson/how-to-graph-1-cos-2x-steps-lesson.html

   The cos(2x) identity can be shown either by graphing cos(2x) on an x-y plot or by using the cos(2x) formula. Cos(2x) Graph. The graph of cos(x) can be analyzed based on several features.

6. Half-Angle Identities - Trigonometry - Socratic

   socratic.org/trigonometry/trigonometric-identities-and-equations/half-angle...

   The half-angle identities are defined as follows: #\mathbf(sin(x/2) = pmsqrt((1-cosx)/2))# #(+)# for quadrants I and II

7. How do you verify the identity: cos^2x-sin^2x=1-2sin^2x? -...

   socratic.org/questions/how-do-you-verify-the-identity-cos-2x-sin-2x-1-2sin-2x

   Recall the Pythagorean Identity. #sin^2x+cos^2x=1# Which can be manipulated into this form: #color(blue)(cos^2x=1-sin^2x)#

8. How do you prove cot^2x - cos^2x = cot^2cos^2? - Socratic

   socratic.org/questions/how-do-you-prove-cot-2x-cos-2x-cot-2cos-2

   see below to prove cot^2x-cos^2x=cot^2xcos^2x take LHS and change to cosines an sines and then rearrange to arrive at the RHS =cos^2x/sin^2x-cos^2x =(cos^2x-cos^2xsin^2x)/sin^2x factorise numerator =(cos^2x(1-sin^2x))/sin^2x =>(cos^2x*cos^2x)/sin^2x =cos^2x*(cos^2x/sin^2x) =cos^2xcot^2x=cot^2xcos^2x =RHS as reqd.

9. cos^2(2x)+sin^2(2x)=? what value is this equal to? - Socratic

   socratic.org/questions/cos-2-2x-sin-2-2x-what-value-is-this-equal-to

   Well the x refers to any number so if your number is 2x, then cos^2 2x+sin^2 2x=1 You can also prove this by using the double angle formula cos^2(2x)+sin^2(2x) =(cos^2x-sin^2x)^2+(2sinxcosx)^2 =cos^4x-2sin^2xcos^2x+sin^4x+4sin^2xcos^2x =cos^4x+2sin^2xcos^2x+sin^4x =(cos^2x+sin^2x)^2 =1^2 =1

10. How do you prove cos2x = 2cos^2x -1? - Socratic

    socratic.org/questions/how-do-you-prove-cos2x-2cos-2x-1

    Use the identity: cos (a + b) = cos a.cos b - sin a.sin b. #cos 2x = cos (x + x) = cos x.cos x - sin x. sin x = cos^2 x - sin^2 x # =

11. Use the power-reducing identities to write sin^2xcos^2x in ... -...

    socratic.org/questions/use-the-power-reducing-identities-to-write-sin-2x-cos-2...

    Use the power-reducing identities to write #sin^2xcos^2x# in terms of the first power of cosine?