> Example 3. Prove that sin? z + cos? z = 1. eiz 2 e2iz - 2+e- -2iz sin? , = Z 2i eiz + e e2iz + 2+ e- -2iz cos? 2 4 sin? z + cos² z = = 1.

Q: cose = +V(sin?0 - 1) O +V(1 + sin?e) O +V(1 - sin?e)

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Q: sin 2x Verify 1+ cos 2x = tan x.

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Q: 2. Solve 2 sec 0 + tan 0 = 2 cos 0, 0<0<2n .

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Q: cos(0 + B) = cos 0.cosB- sin 0. sinB . cos(0 + 0) - cos 20 - cos2e-sin2e 1- cos 20 1-cos2e+ sin 20…

A: We have to prove the trigonometric result.

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: 20 -1 3. sin

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Q: C. If sin A+ sin2 A = 1 and a cos12A +b cos® A+ c cos A - 1 = 0 then b + - + b =? %3D %3D

A: Topic = Trigonometry

Q: If Z-1/v2+i/v2 then the value of conjugate of Z^5=?* O cos(3n/4) O 2sin(5n/4) O 2cos(5n/4) cos(5n/4)

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Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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Q: de -1 < B< 1 (1+B cos 0)² '

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Q: 2) cos² I 6 F/6 sin2 T

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Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: snip

A: sin4θ=sin2θ2=1-cos2θ22=141+cos22θ-2cos2θ=141+1+cos4θ2-2cos2θ=14+1+cos4θ8-12cos2θ=14+18+18cos4θ-12cos…

Q: Use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ≤0 (a) The solution…

A: fx is basically the value towards the y axis.So, we just have to check the values towards y axis.

Q: (b) Show that: cos(x cos 0) = Jo - 2J₂ cos 20 +2J4 cos 40 +

A: Solution (b):

Q: 25-11 2-4s + 8

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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: sin- a. b. undefined cos(-210) C. Cus270 tan450 d.

A: sin17π6=cosπ2-17π6=cos-7π3=cos7π3=cosπ3=12        cos-210∘ =cos210∘ =-32

Q: Find all of the solutions of 2 sin? (x) – 3 sin (x) – 2 = 0 between -T and T

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Q: Which of the following is true? | sin“ zdz (1+ cos a + cos² 2æ)²dx Ob. sin zdr = (1 – cos 2z)²dæ 2 1…

A: Given data: ∫sin4xdx We know that 2sin2x=1-cos2x Therefore, we get…

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: sin' t – cos' t Prove tan?t – 1 cos? t

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Q: If cos (z +) + sin (z -) If cos( x + 6 + sin ( x 3 A, then the number A = %3D

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Q: 8. Prove that tan? 0 + cos? 0 + sin² 0 = sec² 0. %3D

A: Explanation and solutions is given below....

Q: d da cos(3) = O-3 sin (3²) O 32.cos(3²) -3.sin(3²).In 3. O sin (3²) O3 cos(32).In 3

A: Given

Q: 15. Write the equations of two different functions in the form f(x) = a sin[k (x - dᵒ)] + c and g(x)…

A: To write the equation of the given curve that model the function f in the form of f(x)=a…

Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

A: