1) Using Euler's formula prove the following: For any ZEC a) For Sin² z + cos² z = 1 2 b) For any 2₁,2₂ €( cos(Z₁ + Z₂ ) = COSZ₁ COSZ₂ - Sinz, Six Z₂ cos 2 = 0 if and only if Z= I+IK, KE ZZ c)

Q: that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

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Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: Cos I 12. secx + tan x 1. sin x

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Q: 7. a) Prove the identity (cos2z) cos z sin z-2sin³ z b) State all restrictions for tan z. <= tan z

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Q: 5) Given cose = 1/2, determine cos $2 a) H H

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 12) y = 3 cosx + X

A: we have to locate the graph of the function y=3cos(x+π4) to locate this we will put the values of x…

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: 2)Rewrite sin5 x cos³x in terms of cos x: sin5 x cos³x = Rewrite sin5 x cos³ x in terms of sin x:…

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Q: If sin B = 1 E with B in QIlI , find B sin В sin 3 + 22 = 2 5+2/6 sin 10 В sin 3 + 12 5+26 sin 10 В…

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