Evaluate the following leaving the result as an EXACT value. cos⁡(tan^-1⁡(4/3)+sin^−1⁡(−2/5))

Q: establish the following identities: sin3x=(sinx)(4cos^2 x-1)

A: Given,

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

A:

Q: If /3tan0=3sin0,find the value of sin*0-cos²0

A:

Q: Convert to cartesian Sin ()+ tan (0) %3D

A:

Q: csc(sec-1 2) + cos(tan-(-v3).

A: Given data:     The expression for the given function is: csc(sec-12)+cos(tan-1(-31⁄2).   The given…

Q: Find exact positive value of Cos ꆪ = 2/3

A:

Q: if a=cos^2x+sin^4x,then find x

A: Given,

Q: evaluate the following giving exact values when possible: cos(sin^(-1)(y/2))

A: Simplifying the given inverse trigonometric expression to find the desired value.

Q: (1+cos3x)² -dx sin23x

A:

Q: Differentiate  (sin(x+a)/cosx)

A:

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

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

Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

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: What vaule of 0 = sin (0/3 - 10)

A: that is equal to 0=sin(0-10) than 0=sin(-10) such that -10=sin^-1(0) that is equal to zero

Q: Does cos (π/2 - x) = cos (x - π/2)? Explain with examples

A:

Q: Use the identity cos^(2)s+ sin^(2)s = 1 to find the value of x or y, as appropriate. (((2)/(9)), y),…

A:

Q: Find cos(sin^−1(−1/2))

A: Trigonometric