Simplify: sin(x) sec(x)

Q: limg-0 2x sinx 4-4cosx

A: We can find the limit as below, using L'Hospital rule.

Q: cosx/secx+tanx

A: The given expression is:

Q: Evaluate sin(3x) dx. sin(3x) dx (Use C as the arbitrary constant.)

A: sin5(3x) = sin4(3x).sin(3x) = [1 – cos2(3x)]2sin(3x)

Q: sec dx 3 (4 – tan"x) 2

A:

Q: 1-sin'(플-x)

A: The objective is to simplify the expression.

Q: cosh²x-sinh² x = 1

A:

Q: TU (sin³ x)√1 + cos x dx EN

A:

Q: inverse of sec x?

A:

Q: Sec'x 16-tanx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: sin( sec = (x/10))

A: Let sec-1x10=α ⇒sec α=x10 ⇒sin α=x2-100x⇒α=sin-1x2-100x

Q: | sec x tan° x dx

A: on solving with substitution method we will get

Q: How did limx->π/2 = sin (2x) / x become 0?

A:

Q: sec(-x) sin?x sinx X %3D

A:

Q: Evaluate * sin-lr xp= V1- x

A:

Q: |sin³ xdx

A: I=∫0π2sin3x dx =∫0π2sin2x·sin x dx =∫0π2(1-cos2x)sin x dx Let  ⇒cos x=t⇒-sin x dx=dt⇒sin x dx=-dt…

Q: Simplify (cos x- sinx)(cosx+ sinx) sin x cos'x cos x 2 cos x- 1 2 cos x+ 1

A: Given expression, cosx-sinxcosx+sinx

Q: sec 5x tan 5x dx

A:

Q: q-Sin ²1x1 1²/x/_alx

A:

Q: Differentiate. Simplify your answers. f(x) = sin2(3x)

A:

Q: sin 0 = -0.3083 with 0 in QIII

A:

Q: x+2 lim sin - x+6x+8 3 2.

A:

Q: Verify the equation

A: To establish the given trigonometric identity

Q: tan x - dx 2 sec x – tan x 2.

A: Topic:- integration

Q: How did limx->π/2 = sin (2x) / 2x become 0?

A:

Q: Differentiate Sin(x2 +1)

A: Differentiate   Sin(x^2 +1)

Q: 7csc 2X= sec x Sin X

A: topic - trigonometric Identity

Q: sin3x dx 1+ tanx

A:

Q: + sin(x) = cos(x) 4x²

A: Concept:

Q: is x12 an even or odd function? Is sin x2 an even or odd function?

A: Note that -x12=x12. Thus, x12 is an even function.

Q: secx-secx COS x 2+anx sinx-secx

A: Given To simplify sec x -sec x.cos2 x2 tan x - sin x.sec x

Q: x" - x' - 2x = sin3t

A: Consider the given differential equation, x''-x'-2x=sin3t make the auxiliary equation,…

Q: 37. csc x = sin x ; use the Quotient Rule.

A: We will solve cosec x =1sin x - (i) using quotient rulewhich states that dydx=(dydu) (dudx)We will…

Q: cosx + + sin x 3

A:

Q: limx→0 (sin6x)/(tan6x)

A:

Q: simplify  sin(tan^-1(x))

A: Here we simplify sintan-1x

Q: cosx -dx 5+ sin(x) 5.

A: Given: I=∫cosx5+sinxdx For evaluating given integral, we substitute sinx=t…

Q: y- SinX+ tan x3

A:

Q: tan-1x dx. 1 + x2 Use an appropriate substitution to solve

A:

Q: sin-1 Vx dx Vx — х2

A:

Q: tan? x – cot2x = sec2 x – csc? x - tanx-sinx = 1- cosx tanx

A: To prove :- 5.tan2(x) - cot2(x) = sec2(x) -csc2(x)  6. (tan(x) -sin(x))/tan(x) =1-cos(x)

Q: (sec x + tan x)² dx

A: It is basic integration problem  First I have used whole square formula then integrate.

Q: lim 1-cosx/sinx ? x-->0

A: Given:

Q: ∫(〖sec〗^2 xdx)/(1+tanx)

A: Given: ∫sec2xdx1+tanx

Q: tan2(x) sec2(x) dx

A: Given,

Q: Evaluate  ∞  ∫ tan^-1 (x) dx  -∞

A:

Q: Simplify

A: Given:   To determine: simplified form.

Q: B1. By using substitution method, evaluate [5 tan x sec² x dx.

A: To solve the given integral using substitution

Q: (sec 2x + tan 2x) dx

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.