Using Euler's formula prove that cos z=D if and only if z=(pi/2)+(pik), kez

Q: Show that sin-1 v + cos-1 v = π/2 .

A: Given: sin-1 v+cos-1 v=π2

Q: Algebraically, determine all values of 3 with 0 ≤ B < 2π such that cos(2/3) = cos(3) + sin(3)

A: Algebraically determine the values of  of this given problem.

Q: tan²(z) cos³(z)dæ

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Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

Q: Verify sin (x +) = cos(n – x) %3D

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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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: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & sin(A – B) = sinAcosB - cosAsinB…

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

Q: expand the formula for sin(A+B)

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Q: sinr 1. Show that

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Q: FIX) = sin(x+ cos x) -0.5=0 Find F(X), F(x)

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Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: If z = os0+ I sin 0 and y= cos Isin p, then show that %3D 2 cos(@-).

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Q: The relations cosh(i t) = cos t and sinh(i t) = i sin t were discussed in the Excursion. Use these…

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Q: if cos theta = x/2, then 1+that2 theta is equals to?

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Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…