Establish the identity 1-2 sin?o coso-2 sin o= cos (20) Choose the sequence of steps below that verifies the identity. O A. 1-2 sin cos 20-2 sin “e= (cos20-sine)(12 sin 2e) = 1.cOS (20) = COS (20) OB. 1-2 sin 2ecos 20-2 sin “e= (cos20-sine) (1-2 sin 2e) = 1. cos (20) = cos (20) OC. 1-2 sin 2ecos 20-2 sin “e = (cos 20+ sin?e) (1-2 sin 20) = 1. cos (20) = cos (20) OD. 1-2 sin 20...
Prove the identity. 4 cos 40 - 4 sin 40 = 4 cos 20 To verify the identity, start with the left side and transform it to obtain the right side. Choose the correct stop and transform the expression according to the step chosen 4 cose-4 sine = 4 cos 20
Is the following equation an identity? If so, prove it. sin- x - cos x cos x = sin’x - cos x The given equation is an identity. sinx - cos*x = (sin’x)2 – (cos?x)2 = (sinºx – cos x) (sinºx + cos²x) = (sin x – cos2x) (1) = sinºx - cos x. The given equation is not an identity. The given equation is an identity. sin- x - cos*x = (sin?x)2 – (cos2x)2 (sinºx – cos x) (sinºx...
5. Prove the following identity. (sin x + cos x) = 1+sin 2x 6. If cos(x) = , and x E QIV , find the exact value of each of the following. a.sin (2x) b.cos cos()
Establish the identity. 1 - sin 0 cos e + COS 0 1 - sin e = 2 sec Write the left side of the expression with a common denominator. Do not expand the numerator. cos (1 - sin o) Expand and simplify the numerator by rewriting without any parentheses. + cos20 cos (1 - sin o) Apply an appropriate Pythagorean Identity to simplify the numerator of the expression from the previous step. cos (1 - sin o) (Do not...
14. Prove the trigonometric identity: (4) 2) (sin x + cos x)() come an d sin 2x – cas e
sin^2(theta/2)/sin^2 Complete the identity. sin sin2 = ? sinde O e cos? 2 1 4- cos e O_1 2cos e O sin? 2 + 2 cos e
Time series analysis 1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
Prove the trigonometric identity: sin(x + y) sin(x - y) = sin’x – sin? y. Which identity is used to prove it true? sin(x + y) = sin x cos y - cos x sin y All of these. tan o sin e cos e cos? 0 = 1 - sin? 0
Establish the identity 1 - cos 0 sin 0 + sin 0 1 - cos 0 = 2 csc 0. Which of the following shows the key steps in establishing the identity? 1 - cos e sin 0 ОА. + sin e 1 cos e 1 - cos e B + sin e 1 - cos 0 sin e (1 - cos 0)2 + sine 2 = 2 csc 6 sin 0(1 - cos ) cOS (1 - cos 02...