22. Which of the following is the first step in proving the law of cosines? Find the cosine of two angles. Find the cosine of one angle. Use the Pythagorean theorem. Draw a line from one angle in a triangle that is perpendicular to the side across from the angle.

Q: Explain the Pythagorean Theorem, its proofs and applications.

A: The triangle is a polygon with three sides and three vertices. The sum of interior angles of a…

Q: d) Using Demoivre's theorem, show that, if z = e“, then i(:-" - ") sin no = ne N+ 2

A:

Q: Find the order of Z=0 for the following functions: 1) 1+2-e² 2) 6 sin(z ³) + z9-673 3) (e²²-1-7²)…

A:

Q: (a/sinA=b/sinB=c/sinC) prove the law of sines, by any means necessary.

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Q: AU (Bn C))° = (c U Bº)n A°

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Q: p2 cos 20 = 1 COs

A:

Q: -1 cos х ах

A: We can find the answer to the integration in the following steps.

Q: coto cose sece Practice : Prove coce-I Sin e tan e

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Q: -2n 1 9. Evaluate : de 6+ sine

A: Given, ∫02π16+sinθdθ=2∫0π16+sinθdθ Let us take…

Q: Can you write the product as a sum or difference of 8 sin(33b)cos(24b) ?

A: The objective of the question is to express the product of two trigonometric functions, specifically…

Q: cosi in the form x+iy = %D

A: By using Euler's relations we can find the value of cos i

Q: 1. The formula sinusinv 5(cos (u - v) - cos (u + v)] converts a product of sines to a of

A: sinusinv=12cosu-v-cosu+v

Q: csc? a + sec? æ 1 cos x sin z

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Q: vee 0t5 9518 35 cos (Se) dO 1 t Sinse)) -10

A: Apply substitution method to solve the definite integral.

Q: Derive the cosine formula a2 = b2 + c2 – 2bc cos A and the sine formula sin A sin B sin C а b C…

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Q: cot (45°+ e) - tan ( 45°-e) %3D Prove that; 2+an 20

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Q: Use Euler’s Formula to find ii

A: we know that  i=eiπ2 so, ii=eiπ2i=ei2π2                                                  ∵…

Q: (5n arcsin ( sin 6 . (") A) B) 6 C) 6 D) 6. 11n E)

A: Solve the equation

Q: Using csc 8 = ±√1 + cot²0, express csce in terms of cose only.

A: We are asked to express cosec interms cos

Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: Using Euler's Theorem, find expressions for cose and sine in terms of eie and e-ie. You will use…

A: We have to express  and  in terms of  and .

Q: cos a Jsin a

A: Given: ∫cos5αsinαdα =∫(1-sin2α)2cosαsinαdαApply u-substitution u=sinα…

Q: Using Euler's formula ete = cose + i sine %3D Show that el0 +e-10 et0-e-10 cose = sino zi

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Q: cose + sine =1 If a sine - cose and a = 1 b x2 prove that a? b2

A: Given,xacosθ+ybsinθ=1 and xasinθ-ybcosθ=1then prove that:-x2a2+y2b2=2

Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

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A: The objective is to prove, sec(A-B)=cos(A+B)cos2A-sin2B It is known that,…

Q: cos- 0 + sin 0 = 1 COS

A: We know values of basic sin and cos, like sin0 = 0 = sinpi , sinpi/2 = 1 cos0 = 1 , cospi = -1,…