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Q: tan 0 + tan? 0 = sec* 0 - sec² 0

A: This question is taken from trigonometry in which we have to prove the given identity  We can write…

Q: sin x 14) Simplify: sec(x) tan x A) 1 C) sec² x 7n B) tan(x) D) sin(x)

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Q: sin x dx 1- cosx Find

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Q: Sec x cot x sin x

A: We will find the area solution.

Q: cos(: sin@)]=[- sin(esin@)]. * (b) (i) Show that - cose dt

A: We will use product rule of differentiation here

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Q: cos-1 (cosx)= x       where..............

A: Given, cos-1cos x=x

Q: COS X 3) sec x + tan x = 1 - sin x

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Q: •tan(e-x) Given: ex Find: du exdx e-*dx - exdx O -e-*dx

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Q: cos 2x – cos x lim sin?

A: To evaluate: limx→0cos2x-cosxsin2x Solution: We know, cos2x=2cos2x-1  ..(1)sin2x=1-cos2x      ..(2)…

Q: 6 csc(-x) - -6 cot(x) sec(-x) %3D

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Q: 5. * y ↑ Add File 6. * sin x 1 + cos x y = cos² sin x 1 Add File

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Q: sec(2x)cot(2x)dr sin(x)cos(x)

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Q: sec e de 1+ tan 0

A: To find∫secθ1+tanθdθ

Q: COSX 1+Sinx 1+ SinX CoSX (2) See (mx) tan(inx) e a-be

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Q: cos*x sin' xdx

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Q: sec*(x) dx. Vtan(x) a) Vtan(x)[5 + sec²(x)] b) V sec(x)[5 + tan² (x)] c) V tan(x)[6 + tan? (x)] d)…

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Q: sin x (cos x + 4) dx 1+cos?x

A: Given that: ∫sinx(cosx+4)1+cos2xdx

Q: dx sin² x cos²x 10. The value of f; A sinx-cosx+C B. cos x– sin x+C C. tanx-cotx+C D. cotx-tan x + C

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Q: y = sin* 3x – cos* 3x y = csc* x – 21 cot?x y = cot sin

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: sin x dx coos x 6.

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Q: sin(x) Evaluate dx. cos (x) – cos(x) – 2 |

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Q: parts H and I

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Q: |sin? 4x-cos 4x-dx

A: Given that a integration and we solve this integration by using general formulas of the integration.…

Q: sin x cos x 15) Simplify: csc x sec x A) 0 C) tan(x) В) 2 D) 1

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Q: sin(en sin-lx )dr =- cos( sin-!x) +C V1-x? A) True B) False

A: To solve the following integral

Q: sec2 x tan? x + sec x (sec² x + 1) dx sec x tan x (seс? х + 1)

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Q: [(3 csc² x-1)dx a. – 3 tan x – x +c O . – 3 sec x – x +c - 3 tan x + c d. -3 cot x-x+c

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Q: 2 tan-e 1+ sec 0 + 1 = sec 0

A: We solve this problem by using some trigonometric formula 1+ tan^2(a) = sec^2(a) And  As per our…

Q: (cos(3x) sin(x) – sin(3æ) cos(x)) da

A: In the given question we need to evaluate the integral- ∫cos3xsin(x)-sin(3x)cos(x)dx , which can be…

Q: sin- x - y· dx + (tan-(yx-1))xdy = 0 cos-12

A: The given differential equation is x-ysin-1yxcos -1yxdx+(tan-1(yx-1))xdy=0. Simplify to obtain the…

Q: 9. sin cot x. xo a

A: According to our guide we can attempt only one question so i am providing answer for 1st question .

Q: CO SK= Sin X CoS X イメそ2 X= 2anctgt Sin X+ CosX dx= dt 5inイミ イet? ュラナと 2t と? イ2 2dそ (て ーそス 2そ+イーそ?…

A: The function is, ∫sinxcosxsinx+cosxdx

Q: sinh x – cosh x + ecoth r sinh? x - dx

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Q: sin x 6. Evaluate dx. 3 cos x

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Q: sec® tan Od® coso A) tane В sece sec?0

A: topic - indefinite integral

Q: Skill – Express tan? 0 in terms of sec? 0

A: Consider the given trigonometric function. tan2θ The objective of the problem is to express tan2θ in…

Q: cos x + sin x dx Evaluate sin 2x

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Q: y = 4 sin? x +5 cos² x y = sin* 3x – cos* 3x y = csc* x – 21 cot² x y = cot sin

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Q: sin . sin . cos x d. cosz tan E tanz 214 14

A: Given that,

Q: (sec x + 1)(seс х — 1 ес х tan x

A: Explanation of the solution is given below...

Q: y" - y = 10 cos x cosh x

A: Differential equations

Q: cos(x) 3) 1-sin(x) sec(x) + tan(x)

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Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: sec x+ csc x 1+ cot x х

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Q: f. – 1 = tan 0 sec 0 over [0, 2n)

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Q: I+ Sin X COSX 32see* COS X + Sin X

A: This problem can be solved by simplification through trigonometric identities.

Q: cosx sec? x + cos x csc² csc² x csc² x secx cos? x cos x cos x , then 6 f(x)dx_, * f(x) 1

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.