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

Q: How did you know 't' was equal to sin^-1(x)?

A: Given integral,

Q: 2 cos^2 x-sin x -1=0

A: 2cos2x-sinx-1=0⇒1-sinx-2sin2x=0⇒sinx=-1, sinx=12⇒x=3π2+2πn, x=π6+2πn, x=5π6+2πn

Q: I'm suppose to write an expression, and that x is positive. My question is tan(sin^-1(4/x).

A: The solution is shown in step-2

Q: how to verify (1-2cos^2x)/(1-2cosxsinx) = (sinx+cosx)/(sinx-cosx)

A:

Q: solve for x so that sin[2(tan^-1(3/x))]= - 3/4

A: We have given sin2tan-13x=-34 Then,…

Q: Write an algebraic formula for sin[(sin^-1(u)-cos^-1 (v)]

A:

Q: Can someone compute this into decimal form. f'(4)=-sin(4)-3sec²(4) Thank you

A: we already have f'(x)=-sinx-3sec²x so,f'(4) =-sin(4) -3sec2(4)

Q: If sinx^2 =a/b find cos(90-x)

A: See the details solution in below I am consider  sin(x^2 )

Q: Use a half-number identity to find an sinx=(24)/(25) and (\pi )/(2)

A:

Q: solve (sinx)sec^2(x)+(cos x)cosec^2 (x)=0

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Q: 2nd eg- how to derive tan^2x

A:

Q: How did you get the rewrite from sin^2(x)/sqrt(1+cos(x))

A:

Q: Solve for x: sin^2 x -cos^2 x+1=0

A: Solve the equation

Q: Simplify (1/sin (x))+(1/sin^2(x)) in a single reduced fraction

A:

Q: Solve 4 tan x * cos^2 x = 1 for 0 ^ 0

A:

Q: Evaluate tanh^2 (4-4i) sech (2+2i). Express your answer in rectangular form in 4 decimal places.

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Q: Cos(pi/6)=(150-(y^2))/10800

A:

Q: cscxdx 5+ cos²x sin²x

A: Evaluate: I=∫csc2x5+cos2xsin2xdx We know that, cos xsin x=cot x Then, we have I=∫csc2x5+cot2xdx

Q: derivative its actually only cos^12 on the last idk why

A:

Q: Use the reduction formulas to reduce sin^4 θ to only linear powers of cosine (cos(θ) = ”linear”,…

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Q: (Sin X-cos X)^2=1-sin 2x

A: Formulae to note: (a-b)2=a2+b2-2ab. 2 sin x cos x=sin2x. Sin2x+Cos2x=1.

Q: sin[cos^-1(12/13)+tan^-1(4/3)]

A: Given:

Q: differentiate y = sin^3(tet^2) and simplify

A: The given function is y=sin3tet2We have to differentiate with respect to t…

Q: (cos^4 x) - (sin^4 x) = cos2x   verify the identity

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.