1. tan' 4.cos' A + sin' tan 2. sin' A1 + + + cos' 4(1 +tan' 4)-2 tan 3. (cos x+sin x(cos x-sin x)- 2 cos' x 1 4. sin 8-cos' 8-2sin' @-1 5. cos' @+sin'0-(cos @+ sin @1-sin 0 cos 6. tan' @-sin'e-tan' 0 sin' 0 1 sin sin & 7. (tan @ cos 8 cos x sin x 8. (1+ cos x) 1-sin cos 8 sin x cos @ I+ sin & 9. sin 4 10. 1-Cos 4 sin A tan A COs X 11. cosx I+sinx tan x cos x 12. 1-cos x1+ cos x sin x cOs 2.cos x

Q: 1) sin 9) tan-1 (-V3) 11) sin- 2

A: Given! 7)sin-1(-1/2) 9) tan-1(-√3) 11) sin-1(-√2/2). Repost the next parts.

Q: How do I simplify (9-sin(x))(4-3cos(x))-(9cos(x))(3sin(x))

A: Given that: (9-sinx)(4-3cosx)-(9cosx)(3sinx)

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Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: 12) sin-1 -1 14) tan 0 V3 16) sin-! |

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Q: Find tan'e de cos*e 33. sin o 36. Cos

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Q: Prove that (sin^(2)B-tan^(2)B)/(1-sec^(2)B)=sin^(2)B are identities

A: Given, sin2B-tan2B1-sec2B=sin2B Consider the left hand side. sin2B-tan2B1-sec2B

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Q: 6. cos x(csc x secx) secx) cotx

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A: When theta is between 0 to 360 degrees, then 2theta is between 0 to 720 degrees. We use sin inverse,…

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A: Solution:-

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A: Please find attachment for the details solution

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A: I have stated the used formula in the solution

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Q: If tanlas = 3 and tan (6) =2, where olas and CL6, find sin (a-6)

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Q: 5(a) Is 1+tant=sint(csct+sect)TRUE for all values of t? If YES, prove the identity. Otherwise,…

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Q: sin(2 tan " (-} ))

A: Given,  sin2tan−1−83Formula→2tan−1x=sin−12xx2+1                 sinsin−1x=x

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Q: 1-sin' x 3D sin.x 6. cosxcotx

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Q: sin2 (4) %3D cos2 ( ) O csc2 () csc2 () cos2 ( 4)

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Q: 0 a "/2 ((+ cos@)-1)sin@d0 + a |((1+ cose) - 1)sinede 3 3 a ("/2 (1+3cos@+3cos 0+ cos 0-1)sin@de a3…

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Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

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Q: 1) cos- 1 2 3) sin-1 V3 5) cos-.

A: As per our guidelines we are supposed to answer only first three parts.kindly repost others part as…

Q: Prore each of the following identities: (ii) (1+cot 0)sin 0 1 1 (1) (1-cos 0)cosec o=1 rie-1)cot 0 1…

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

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Q: tollowing. 1. sin(sin)

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Q: tan 0 cos²0 = 2 tan 0 cos² 0 - tan 0 1tan²0

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.