1 (a) sin- (b) cos (-) (c) tan-' (- V3) 3. 2.

Q: Is sin-1 x the same thing as1/sin x?

A:

Q: Reduce sin 0 to an expression involving only function of multiples of 0, raised to the first power.

A: Given, sin4θ  We have to reduce sin4θ to an expression involving only function of multiples of θ,…

Q: Prove the identity. sinx 1+ cos.x 2 cscx 1+ cos.x sinx

A: Given, The identity  sinx1+cosx+1+cosxsinx=2cscx We have to prove the identity.

Q: Verify the identity: (cos 3x - cos x)/(sin 3x + sin x) = -tan x.

A:

Q: Express sin 5x cos 3x as a sum of trigonometric functions.

A: Given           sin 5x cos 3x

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: The given identity is, sin -x sec -x=-tan x. The objective is to verify the identity by transforming…

Q: If sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

A: Given sinx-cosx=15Squaring the equationsin2x+cos2x-2sinxcosx=125

Q: express as an algebraic expression in terms of x. sin(arctan(x))

A:

Q: If sinX = -1/3 and cosX is positive, determine the exact value of cotX.

A: We know, cosx= ±√(1-sin2x) cotx= cosx/sinx

Q: Find the derivative of tan−¹(x).If you use the identity 1 + tan²(x) = sec²(x), you can write the…

A:

Q: Verify identity tan2 2x + sin2 2x + cos2 2x = sec2 2x.

A: To verify: tan2 2x + sin2 2x + cos2 2x = sec2 2x WKT cos2x+sin2x=1 x refers to any number, Replace x…

Q: -sin^2(x)=cos(2x) from [-pi, pi]

A:

Q: how can you express cos x in terms of tan x?

A:

Q: Find sin x if sin x – cos x x = 3 sec x

A: Consider the given trigonometric expression, sinx-cosx=13 now square both side of the equation,…

Q: Find an equivalent expression for sin 4x in terms of function values x sin 4x =

A: power series of f(x) about x =a is  f(x) = ∑h=0∞ fn(a)n! (x-a)n ------- (*)

Q: Solve for the values of sin2x, cos2x and tan2x when tanx = 1, on 0≤x≤

A:

Q: Find the exact value of the expression. tan(sin−1(-1/2)-cos-1(-1/2))

A: According to the given information it is required to calculate the exact value of the expression:

Q: Find sin x if cot x=-(√3)/2 and cos x (less than) 0

A: We will find the value of sin x.

Q: Find the exact value of sin(x - y) if sin x = 3 ≤ y ≤ 2. on ≤x≤ and sin y=-3 on

A:

Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

A:

Q: Compute sin(sin-(2/3)) O 2/3 This quantity does not exist.

A:

Q: Suppose tan x = -4 , where < x < n. Find the exact value of sin(2x).

A: see 2nd step.

Q: sin2x+cos2 for x = 55 degrees.

A: Apply trigonometric identity cosA=sinπ2-A to rewrite the expression. sin2x+cos2x=sin2x+sinπ2-2x…

Q: If x= ln (sec θ +tan θ) , show that sec θ = cosh x .

A: It is given that  x= ln (sec θ +tan θ)

Q: Why is cos(sin^-1(x)) equal to sqrt(1-x^2)?

A:

Q: What is the exact value of tan(sec-"(-"),

A: This is a problem of the fundamentals of trigonometry. Based on the general formula we will answer…

Q: Solve sin x − cos x = 1 if 0 ≤ x ≤ 2π.

A:

Q: Find the exact value of the expressio sin(cos-(금)-ton-1(1) (€) tan 4 4

A:

Q: 4. Find the exact value of sin if cose 2 3 and e is in QIII. cose =-- |

A: According to question,Given conditions,cos θ = -35,θ is in third quadrant.

Q: 4 If cos x = csc x < 0, then sin 2x = cos 2x = tan 2x = ||

A:

Q: /2 sin-1 (-)

A:

Q: What is the exact value of cos (tan ¹(-1)) 2 -? sin cos 08-¹(- +/-))

A: We have to find the exact value of costan-1-1sincos-1-32.

Q: If cos(x) = - and sin(y) = - with tan(x) > 0 and cos(y) < 0, algebraically compute the exact value…

A:

Q: Verify the identity: cot(-x) sin x = -cos x

A: cot(-x)=-cot(x)cot(x)=cos(x)sin(x)

Q: Verify the identity : sin(x + π)/cos (x + 3π/2) = tan2 x - sec2 x

A:

Q: 8. If sin x- cos x = 3, find sin x sec x

A: given: sinx-cosx=13 to find: sinxsecx

Q: Simplify 3 TT sin-(sinx) if TSXS 2 - -x- T ーX π-X x- π

A: Given, To solve  sin-1(sinx)  if π≤x≤3π2

Q: sinx In (2) cos:

A:

Q: Differentiate x sin-1 (x) with respect to sin¯'x. х.

A:

Q: . Evaluate cos 3x sin² 3x dx

A:

Q: What is the equivalent to sinθtanθcscθ for all values of θ for which sinθtanθcscθ is defined?

A:

Q: if sinx=1/8 and x is in quadrent 1, then cos(180-x)=???

A: Simplify cos(180-x),

Q: solve, sin(4x)cos(6x)-cos(4x)sin(6x)=-0.35 x=??

A: solve, sin(4x)cos(6x)-cos(4x)sin(6x)=-0.35

Q: Find tan 0 if sin 0 = 3/4 and 0 terminates in QI. tan 0 =

A:

Q: If csc 0 = 2, calculate an e sec () sin² 0 exactly.

A: We use cosec x=1/sinx and tanx=sinx/cosx,secx=1/cosx. See 2nd step.

Q: Find sin (x/2) cos(x/2) tan(x/2)

A: Given information is :

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.