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

Q: Sinxtsina3x COSX+ COS 32 tan 22

A:

Q: Verify the identity : 1-cosx sinx = 2 csc x sinx 1– COsx 2.

A: Given- 1-cosxsinx+sinx1-cosx=2cscx To verify- The above identity. Identity Used- sin2x=1-cos2x

Q: (sing -Cosx)=1-Sinx COSX 2.

A:

Q: [sin³ 4x cos 4xdx

A: We can find the answer as below.

Q: Verify that (sinx-cosx)2=1-sin(2x)

A:

Q: (1) / in | (sin-x)° dr

A:

Q: How would I simplify secx-cosx/sinx?

A:

Q: 2. Sinx- Cosh

A:

Q: simplify sin 2x/1-cosx   Not sin^2x its sin2x

A:

Q: Determine the exact value of sin 225°. approximations will NOT be accepted.)

A:

Q: How would I simplify (1-sin2x)secx?

A:

Q: If you need to review them, here is a link to the DQ Instructions. Show and briefly explain your…

A:

Q: Find the first derivative: y = 3 arcsin(cos 2x) O -7 О-5 O-4 O-3

A:

Q: Prove the equation Sin^2xcos^3x=(sin^2x-sin^4x)(cosx)

A:

Q: Compute without using a calculator.

A: Given sin-1sin-5π6

Q: Find 7 sin (7x) dx

A: According to question,Given Integral,Let I = ∫7 sin27x dx

Q: Find 7 sin² (7x) dx

A:

Q: Express sin6 Oin terms of powers of sin Oonly

A: We have given,  sin6θ we have to express it in the term of sin only.

Q: Simplify. sin 2x · cos 3x – cos 2x · sin 3x

A:

Q: What is the exact value of sin4)-sec(-) -4+/2 A 2 4-/7 B -4-/7 2 4+/7 2

A:

Q: Find the possible values of x in |coshx -sinhx| = 2 Isinhx coshx

A: Given,           coshx-sinhxsinhxcoshx=2

Q: cotx (1- cos 2x) = sin 2x

A: Formulae used: 2sinx cosx = sin2x cotx = cosxsinx cos2x = 1-sin2x

Q: Describe the technique for finding ∫ sec5 x tan7 x dx. Do not integrate.

A: Given ∫sec5x tan7x dx

Q: Without using any tech, put these radians in increasing order  sin(1), sin(2), sin(3), sin(4)…

A:

Q: As 0 increases from 90 to 180 degrees, describe the value of Sine over this interval.

A: The sine of an angle in a right triangle is equal to the ratio of the opposite side length to the…

Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: How can I find tan inverse of 3/2 or any number larger than 1 without a calculator?

A: We have to find value of arctanx,any value of x which is greater than 1.

Q: If the value of sinx 4,0≤x≤, the value of cosx within the same domain is:

A: Given that sin x = 47, 0≤x≤π2 find the value of cos x, 0≤x≤π2 The domain of cosine and sine function…

Q: How would I simplify (1+sinx/cosx) + (cosx/1+sinx)

A: Answer and explanation is given below

Q: I want all the laws of trigonometric functions and the laws of their integration

A:

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: Express sin 2θ in terms of x = sin θ.

A:

Q: S(sec; - sin) do

A: We know that integration power rule is  Integration of (xn) = xn+1/n+1.   Here i attached the…

Q: If cosx = -* and tan x> 0, the value of sinx is

A:

Q: 3 sin3xcosxdx (COSX

A:

Q: If tanx = 2/2 and a < x < find cos- 2 %3D

A:

Q: Find an approximate value for sin179∘.

A: Consider the given angle is x=sin 179o . Use the approximate formula for small Δx where  Let…

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: Differentiate sin3 x

A:

Q: cos 2x cotx-1 1+sin 2x cotx+1 20

A:

Q: cos 2x sin2x Cotx

A: Solution: The objective is to find the value of the given expression

Q: Solve sin 2x - sin x = 0 if 0 ≤ x &lt; 2π.

A: Given:sin2x-sinx=0

Q: If 16(sinx) + 16(cosx)2 10 then x-.. %3D

A: Given that 16(sin x)2+16(cos x)2=10. That is 16sin2x+16cos2x=10. We have to find x value.

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: please show all steps of how to verify identity  (1-cosx)/(sinx)   +   (sinx)/(1-cosx)  = 2cscx

A:

Q: Determine the exact value of sin 225°. (Decimal approximations will NOT be accepted.)

A:

Q: Ok, I see how sinx derives to cosx using that formula sin^2x + cos^2x = 1, thx it helps

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.