6. Let z1 = x1 and z2 = x2, with x1, X2 real, and the relationship ei(x1+*2) = etx1ętx2 to deduce the known trigonometric formulae sin(x, + x2) = sin x, cos x2 + cos x, sin x2 cos(x1 + x2) = cOS x, cOS X2 sin x1 sin x2 and therefore show sin 2x = :2 sin x cos X cos 2x cos? x – sin? x

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

A:

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. sin xsin ydx+cos x cos ydy = 0 2. dr = b(cos Odr+rsin Ode) 3. x cos² ydx + tan ydy = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 9 If f(0) = cos 0, ·cos 02· cos 03 ... cos 0n .... .·. f' (0) f (e) Show, {tan 01 + tan 02 + tan 03…

A: Given that we have to prove where

Q: Verify the identity. 4 cos(sin-1 x) = V 16 – 16x? Let e = sin-1 x = sin e = x = X. * Thus, 4…

A: Explanation of the answer is as follows

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

A:

Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

A:

Q: 4. The value of fx sin(x²+3) dx Acos (x²+) + C C. cos (x²+)+C B. -cos (x²+)+C D. -cos (x²+) + C

A:

Q: Compute / sin æ · cos1º æ dæ. 1 Cos1 11 2 -cos' x + 13 1 cos17 x + C 17 1 cos" x + g11 cos13 13…

A: To evaluate ∫sin5x cos10xdx

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

A:

Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: Compute and * for the equation sin(x)e +2z²y = cos(z). 4xz COS ду

A: sinxe4xz + 2z2y = cosz∂z∂x = ?∂z∂y = ?   While calculating ∂z∂x  variable y will be considered as…

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: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

A:

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

A:

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

A: Sol

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

A:

Q: - cos(x) - 1, choose all values of c in the interval (, 5 For f(x) guaranteed to exist by Rolle's…

A: For fx=-cosx-1, choose all the values of c in the interval π2,5π2guaranteed to exist by Rolls's…

Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

A:

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

A:

Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

A:

Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

A:

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

A:

Q: ,2 Compute x² cos(x³ + 3) dx

A:

Q: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

A:

Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

A:

Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

A:

Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

A:

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

A:

Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

A:

Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

A:

Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

A:

Q: . Consider the function ƒ(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [o,]. If we…

A:

Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

Q: 2. Consider finding the root of f(x) = e*(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A: 2 Given function is fx=e−x3.2sinx−0.5cosx. We have to find the roots of the function fx on the…

Q: Q6:- Prove that: y" = 0 if (cos y3csc COS

A: To prove : y'' =0

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A:

Q: -1 Find y' where y = 22 sin-(cos (9 æ)) – tan (6 æ) Answer: -198 sin(9 x) 1 || V1-cos2 (9 æ) 1+36 x2…

A: To find y'

Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

A: