2 Simplify (sin ½x cos ½x) *

Q: Verify that the equation is an identity. 2 sin x tan 2.r = 2 cos x - sec x

A:

Q: las to rewrite the identities. b. sin(8x)-cos(8x)

A: a) We have to use the formula

Q: Verify the identity. sin +0 = cos 0 0 2

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Q: Solve the 6 sin>x -Cos X5 trig guatin

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Q: Which of the following expressions does not equal 1? sec²x - tan²x csc²x - cot²x sin²x - cos²x

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Q: Prove that sin 4A = 4sinA cos³A - 4 cosA sinA.

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Q: 57T then 4° If 0 %3D - sin(0) equals cos(8) equals tan(0) equals sec(0) equals

A: Using trigonometrical identities.

Q: Evaluate : 1) | cos x 3) [ cos x 2) [ ,cot ydy sin' x 1+ sin x 7/4

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Q: 2n sin(30) do 4. Jo 5+cos²(0)

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Q: 7. sin? x + 2 cos x = 2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Verify the identity.

A: We have  cosx-5π2=sinx   It is known that cosA-B=cosAcosB+sinAsinB   Consider LHS:…

Q: 12. sin (3x + 10)° = cos (x + 24)°

A: (12) The equation is given by sin3x+10° = cosx+24° To evaluate : The value of x

Q: Evaluate 3 .9 sin (15x) cos (15x) dx.

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Q: what is the value of x if cos(5x+10)°=sin(4x−1)

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Q: Determine the exact value of sin(75°). 1 O v6-v2 4 4 O V3 2

A: SOLUTION-

Q: simplify a. sin^2(3x)+cos^2(3x) b. cos^2(3x)-sin^2(3x)

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Q: Find the value of  x cosx = cos600 cos300 + sin600 sin300

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Q: evaluate using the appropriate method or combination of methods.

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Q: Evaluate: sin rv1- 4 cos² x dx. /9 – (In r)² Evaluate: dr.

A:

Q: Evaluate ∫  (sin8t +20 cos9t) dt.

A: Use the formula for the integration of sin t and cos t. ∫sin t dt=-cos t+c ∫cos t dt=sin t+c

Q: A = -, find sin 2. If 90° <0 < 180° and cos 0 :

A:

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin22x = 1- cos?2x В cos²2x = 1-…

A: Check the identities

Q: 14. cos (x+ 15)° = sin (¼x + 60)°º

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Q: Find 13 sin(82)da [13 sin(8x)dz = +C

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Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: Express the product sin 7x cos 3x as a sum or difference.

A: Given information: The given expression is sin7xcos3x. Concept used: 2sinAsinB=sinA+B+sinA-B…

Q: Determine the value of 0 in sin(40 + 2°)csc(30+5°) = 1 O 3° O 4° O 5° O 2°

A: sin(4θ+2°)csc(3θ+5°)=1sin(4θ+2°)×1sin(3θ+5°)=1

Q: 5T in terms of sin(x) and cos(x) 3 Rewrite sin ( x +

A: sin(x+5π/3)

Q: Solve for 0 ≤ θ &lt; 2π. sin θ = cos 2θ

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Q: 2 Cos4 Sin (sinz) de

A: Consider the integral  ∫cosxsin2sinxdx

Q: Find cos(sin^−1(−1/2))

A: Trigonometric

Q: (4) |sin² 0 cos0 d0

A:

Q: Cos2x dx (1-sin2x)4

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Q: Choose the equivalent sin'x O 1- cos-x

A: Given sin^2(x)

Q: Simplify cot^2 x + sin^2 x + cos^2(−x)

A: The trigonometric equation is cot2x+sin2x+cos2(−x).

Q: b) SE cos(3x) sin(3x) 18

A:

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: A cos?2x=1– sin2x 1+ cos4x & 2…

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Q: 14. An expression that is equivalent to sin 2x is 1- cos 2r tan r

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Q: Express as a sum or difference.3 cos x sin 2x

A: To express: The expression 3cos x·sin 2x as a sum or difference. Given: The expression is 3cos x·sin…

Q: Show that sin x – cos x< V2 V2 -

A: Take RHS first and work on that:

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin4x, 1+ cos4x &- 2 (А) (B) cos?2x…

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Q: Solve for x 1. xcos60° tan45° = 2 - csc? 90° %3D

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Q: 1 Q:Evaluate: 3 sin x+cosx

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Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: 2. Cos4 Sin (Sinz) de

A: We have to solve

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

A:

Q: Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's…

A: This question can be solved using the De Moivre's theorem which says eix=cosx+isinx

Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.