Q2\ Choose the correct answer from the following options 2 sin^2x = * cos 2x O cos x cos 3x O sin x O sin 2x sin 3x O sin x cosx O sin2x Yorhich of the following statements a O O

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: If e /2i =sin2 then z = 2i In(sin2) + 4k TI - 2i In(sin2) – 4k TI - - 2i In(sin2) + 4k TI - -2…

A: Use the principal log to find z.

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: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

Q: verify the results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

A:

Q: Prove sin 2x cot x (1 - cos 2x)

A:

Q: Approximate all solutions to 8.cos(x)2 –6.cos(x)+1 in the interval [0°,360°) X= degrees Round your…

A: The given equation is quadratic in cosx.

Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

A:

Q: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

A:

Q: 3. If cos x = -, find sin(2x) given sin x < 0. -3 O O

A:

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

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: Suppose cos x = - , where n < x < * . Find the exact value of cos(x – 4) . COS

A: cos(A-B)=cos A cos B+ sin A sin B

Q: Prove that sin 5x + sin 3x/4 sin x cos^3 x - 4 sin^3 x cos x = 2 cos x

A: Given: sin5x+sin3x4sinxcos3x-4sin3xcosx

Q: 3)* dr sin 20 Find if r = do 1+cos 20 dr dr d0 1+sin 20 do 1+ cos20 OOption 3 O Option 4 de sin 20…

A:

Q: Find if r = sin[cos(-0)]. de dr = sin 0 cos(cos 0) de dr cos[sin(-0)] de Option 3 Option 1 dr dr sin…

A: This question is based on application of Derivative.

Q: Find the value of cos(4x) if = 4. 3 1-cos(x)-sin(x)

A: trigonometry

Q: Show that 3(sinx-cosx)*+6(sinx + cosx) +4 (sin r+cosx) = 13

A: Since multiple questions are asked, Answering first one. Repost with other question if you want to…

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

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 –…

A:

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

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

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

A:

Q: sin 3xdx Evaluate: S 4+cos?3x

A:

Q: Using the result of the previous question, explain why 1 n sin" xdx = - sin"-2 xdx. n and hence show…

A: The given problem is to show the result of given integral with using the given integral result.

Q: -1 V3 2 Blank 1: CoS Blank 2: tan- (-) 3 (sin (-4)) Blank 3: sec 2 Blank 4: cos- (cos (*)) Blank 5:…

A: We have to find the exact values .

Q: 51 |x* sin 3xdx 2 53 [x' sin 3xdx 55 sin 3xsin 2.xdx

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

A:

Q: Which expression is equal to sin^4⁡x−cos^4⁡x / sin^2⁡x−cos2^⁡x using identities?   −1   2   1…

A: Topic- trigonometry

Q: 1) Solve (tan(x)−1) (3tan(x)+√3) over [0,2π) 2) solve sin2(x) − sin(x) = 0 over [0,2π

A:

Q: 7. Show that sin (+ x) = -cosx.

A:

Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: 4. Given cos 2x = cos²x - sin² x. (Optional) (a) Verify sin 2x = 2 sin x cosx. cos 2x, (b) Express…

A:

Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A sin²2x =1– cos2x…

A: We need to choose correct option.

Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

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

A:

Q: Prove the below 3 sin 4x 4 cos' x sin 3x + sin' x cos 3x |

A:

Q: 4 dx 1– cos(4x)

A: We to evaluate the integral ∫4 dx1 - cos 4x

Q: Prove: sin² x + 2 cos²x − 1 = cos²x -

A:

Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

A:

Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

A:

Q: 11. True or False. sinh²x = - -+cosh (2x) O a. False. Correct answer is +cosh (4x) O b. False.…

A: topic- trigonometric identities

Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A None 1- cos4x…

A:

Q: Prove the below 3 sin 4x 4 cos' x sin 3x + sin' x cos 3x

A:

Q: Approximate all solutions to 8-cos(x)² – 6·cos(x)+1 in the interval [0°,360°) x = V degrees Round…

A:

Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…

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.