1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

A:

Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

A:

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

A:

Q: Find all values of x in the interval [0, 2?] that satisfy the equation. 6 cos(x) + 3 sin(2x) = 0

A:

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

A:

Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

A:

Q: Q3-Prove that (cos303cos³ 0-3cos 0 sin? 0)

A:

Q: 2+7 sin cos z zp-

A: Given: ∫2+7sin3zcos2zdz

Q: 10. 3 J√cos z sin ³ zdz COS

A:

Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

A:

Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

A:

Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

A:

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

A:

Q: 8. Find all solutions of the equation in the interval [0, 2n) a) sin(x+ t/2) - cos?x = 0

A: The trigonometric equations are:          sinx+π2-cos2x=02cos2x+7sinx=5 The interval for the…

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

A:

Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

A:

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: find the exact value of the expressoion:   cos[sin-1(1/2)]

A: We have to evaluate the value of

Q: Express f (0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0.

A:

Q: 3.16. Show that 10 (1 – i)49 (cos + i sin ) (8i – 8/3)6 - V2. -

A:

Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

A:

Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

Q: 21) (1 + cos 9t) 2 sin 9t dt

A:

Q: Find all solutions to 2 cos(0) = V3 on the interval 0 < 0 < 2n %3D 0 =

A:

Q: Why is I cos 0 |never greater than 1 in the first place?

A:

Q: What mathematical result is applied to prove that sin^2(e)+cos^2(0)=1?

A:

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 23, sin 50° + sin 40° 23. sin A VZ cos 5° B 2 cos 10° 2 cos 5° D V2 cos 10°

A: Trigonometric identity: sin x+sin y=2sinx+y2cosx-y2

Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc…

A:

Q: 2. (sin20 - 2p cos O) dO = 2dp

A:

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

A:

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.