1-Sin 2x Sin Ge)-Ces c -Sinc- Cosk 1- Sin 2x - Sinx+ Cosc Sinx-Casx -Sin x +CUIX - Sin le)(-Sine + Cosx) Comeh (Sinac-cosx)(-Sinx + Cosac) Sinx +Cos ax +sinzx Sinx-15n2C Sin?x + 2cos x Sinx- Cost x

Q: (1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: 1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

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Q: 2) sin- 0 4) cos 6) cos-1 | V3 8) tan 3 -1 -1 10) cos

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Q: gral. cos 7x cos 4x dx ㅇ응 cos 3x + 숲 cos 11x + C ㅇ sin 3x + sin 11x+C 1 sin 3x - sin 11x +C

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Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

Q: 5TT 2. Cos 6. 2п Cos 3 + sin sin 6 - - - 3 一。

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Q: establish each identity

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. 5. xcos x (sin'x - 2sin'x + sin°x)(cosx)

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Q: 2-[ ( 6 sin 2t – 5 cos 2t ) 6. 3+2S 4-1

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Q: 2. Express sin40 and cos40 in terms of powers of sin 0 and cos e only, respectively.

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Q: Help me solve

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Express sin 20 in terms of x, where x = sin 0. A. sin20 = sin? 0 = x² 2x(1– x² )² C.sin20 =…

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Q: a) cos 0 = , 0 is in Quad. I -5 b) sin 0 13' Ө is in Quad.IV X = ‚y = „r = 5 X = - y = „r = 13 tan 0…

A: This question is related to polar coordinates

Q: 6) 1-cosx %3D 1+cosx (cotx - cscx)2

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Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: 3. * 2+7 sin3x cos2x 2 tan x+ 7 sec x +7 cos x +c C 2 tan x-7 secx +7 cos x +c 2 tan x + +7 cos x +c…

A: The integration of the integral is  (2+7sin3x) /cos2x.

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: True or False sin ( 20) has two equivalent forms: 2 sin 0 cos 0 and sin² 0 – cos 0

A: Given statement is, sin2θ has two equivalent forms: 2sinθcosθ and sin2θ-cos2θ.   The objective is to…

Q: 16) tan cos -1 V299 18) cos tan-- V57 20) sin cos 19 3/5

A: topic - Inverse trigonometric functions

Q: Simplify - 2sin(2 – x)cos(2r + 1). O cos(x + 3) – cos(3x – 1) O sin(1 – 3x) – sin(x +3) O sin(3x –…

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Q: 11) cos x csc X tan x - 1 11) 12) cos2x - sin2x = 1 - 2 sin²x 12)

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Q: 8. Simplify: cos(5x) cos(2x) + sin(5x) sin (2x) B) sin (5x) cos (7x) C) sin(3x) D) cos(3x) CoS

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Q: 5/2 Sin'2 cos3x

A: write ∫sin52xcos3xdx as ∫sin52xcos2xcosxdx. Use the identity sin2x+cos2x=1. So,…

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: (1 + cos α)(1 − cos α) = sin2 α (1 + cos α)(1 − cos α) = 1 −(     )=sin2α

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Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9x)-cos(4x) +c Select one: True O False

A: topic- indefinite integral

Q: 1/sin ^2x + 1/cos^2x=1/sin^2x cos^2x

A: 1/sin ^2x + 1/cos^2x=1/sin^2x cos^2x

Q: x = -30°, cos 2x = 1 - 2 sin2 x 1 + 2 sin 2 x 1 - 2 sin 2 x 1 - 2 sin x 1 + 2 sin x

A: This question is based on Proving a Trigonometric equation.

Q: cos 2x+1 sin 2.x 7. Prove that sin 2x 1-cos 2x

A: The trigonometric of an acute angle in a right triangle express the relationship between the angle…

Q: 1 1-Sine Cose Cos0, tan0 in terms of u. (ans.:(u-1/(u+1): 2w(u+1):(-1/(u+1)) 1+ Sine 10. If u= prove…

A: Given thatu=1+sinθcosθ ..........(1)to prove that1u=1-sinθcosθ

Q: -5 cos 2B cos 6B -5 cos 4B + 5 sin 8B -5 cos 8B – 5 sin 4B 2 2 -5 cos 4B – 5 sin 8B -5 cos 4B – 5…

A: Solve : -5cos2Bcos6B Use formula = [cos(a-b)+cos(a+b)]/2

Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: sin can be expanded to: sin 4 COS 2 cos - sin sin 2 O sin 4 sin -cos - + cos –sin 2 4 2 O sin + sin…

A: Given: sinπ4+π2 To find: expand the given trigonometric expression. The formula for…

Q: (sin 4z + cos 4) O 2+ sin 4I COs 4r O 1+2 sin 4x cos 4x O 4+ sin 4I COs 4x O 1+2 tan 4x cos 4x O 1-…

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Q: Cos(5x) cos(2x) + sin(5x) sin(2x)

A: Given: Cos(5x) cos(2x) + sin(5x) sin(2x)

Q: 1+cos 4x Express without double angles. sin 4x O (cot a + tan x) O ÷(cos x 글 (cos sin x) - O (cot a…

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Q: Establish the identity.

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Q: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

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Q: 1.) ∫(sin3x+cos2x)²dx

A: Evaluate: ∫sin3x+cos2x2dx

Q: sin + 4 4 can be expanded to: sin sin 4 4 cos cos 4 o sin - cos 4 sin 4 sin 4 o cos -sin 4 + cos 4…

A: Solve the following

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

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Q: 9. ytan x² a. 2xsec³² 10. y=sin x + 5 cos x a. posx–5sinx b. 5 cosx+sinx b. 2x sec 2 x² c. xsec²x²…

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Q: 13л +i sin 16 5л +i sin 8. 13л 5л Let Z1 = 10| cos and Z, = 2| cos 16 8

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Q: (A[cos(6) - 3 cos(3) + 2] + B[– sin(6) +3 sin(3)] = 2, A[sin(6) + 3 sin(3)] + B[cos(6) – 3 cos(3) +…

A: Given that, Acos6-3cos3+2+B-sin6+3sin3sin3k+Asin6-3sin3+Bcos6-3cos3+2cos3k=2sin3k

Q: cosh(3i)is equal to O -cos3 O cosh 3 cos 3 O sin 3

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Q: 18. Prove tan (0)+1= sec (0) 19. Solve: 2cos? (3x) + 5cos (3x)- 3 = 0 a. b. 4 cos

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Q: [cos 20-i sin20cos 30+ i sin301² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De Moivre's theorem?

A: We have to solve given Questions.

Q: 4. cos' (sin (7 /6 )) 5. sin 1 (cos (π/ ) 6. tan (sin (3n/2))

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Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.