15. Simplify the expression. tan(sin¬'x) b. sin(tan-'x) а.

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: Differentiate. y = In Sin x  - 1/2Sin2 x

A:

Q: 28. tan (2x) sec (2x) dx

A: follow the procedure given below.

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 3. Find the value of sin(2x) given that sin x = and x is in QII.

A:

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

A:

Q: cos(4x) – cos(8x) tan(2x) tan(6x) cos(4x)+ cos(8x)

A: We have to proof

Q: 5) 3tan-1x + sin-x = 4

A:

Q: verify the identity: sin(x+y) + sin(x-y)         = tanx cos(x+y)+cos(x-y)

A:

Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

A:

Q: Find sin 2x, cos 2x, and tan 2x if cosx = 2 and x terminates in quadrant I sin 2.x cos 2x tan 2.x

A:

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

A:

Q: Evaluate ∫sin2 x cos4 x dx.

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx=- 1 and x terminates in quadrant II. sin 2x %3D cos 2x %3D…

A:

Q: 5. y = sin² (In .x)

A:

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: Verify the identity. cos x = sin x sin 2x + cos x cos 2x

A: we have to verify the identity

Q: Differentiate Sin (m sin-1 x)

A:

Q: 4. y = tan¬1(3x) cos 1 4x 5. y =

A: To determine the derivative of given functions. Here we will use the following formulas-…

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: Differentiate a $sin "(z) with respect to sin x.

A: We will find out the required value.

Q: Evaluate ∫sin 3x cos 5x dx

A: Given: I=∫sin3xcos5xdx                                                          ...1 for finding…

Q: If tanh(x)=5/13, what is the sinh(x)?

A: Answer is sinhx=5/12. Explanation is given below..

Q: How can I rewrite: sin(cos^-1(x)*cos(tan^-1(y)-cos(cos^-1(x))*sin(tan^-1(y))  as an algebraic…

A: Given expression

Q: If x is in radians, the derivative of sin(x) is cos(x). Find the derivative of sin(x) when x is in…

A: Given, sinx°  We have to find the derivative of  sinx°.

Q: 6. When defining the inverse sine function, the domain of y = sin x is restricted to -÷<xs. a. Why…

A:

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

A:

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

A:

Q: ( tan( tan3x)dx Evaluate: cos²3x A -In |sec(tan3x)| + C 3 |cos(tan3x)|+C B © --n |sin(tan3x)|+c O…

A: Evaluate: I=∫tantan 3xcos2 3xdx

Q: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

A:

Q: 2. Describe a way of evaluating sin° x dx.

A:

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

A: To prove  sin (3π/2 - x) = -cos x

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: Evaluate sin 3x cos 5x dx.

A:

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Differentiate  x sin−1(x)  with respect to sin−1x.

A: Using derivative of one function w r to another function.

Q: Verify the identity. sin x- cos -x=2 sin x- 1

A: We have to verify the identity  sin2x - cos2x = 2 sin2x -1  To verify the given identity we will use…

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

A:

Q: 05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use…

A: Find the derivative sin2x

Q: 3 cos xdx 1-sinx

A:

Q: 9, 9. tan 2x dx 0.

A: Integration basically means to find the integrals, i.e., to assign numbers to function in such a way…

Q: 15. Evaluate | sin° x cos xdx 3

A:

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: Find x where 0 ≤ x ≤ 2π. cos x - tan²x = 1

A:

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

A:

Q: 1. Verify the expression cos(x) + sin x tan x = secx.

A: Given, cos x + sin x tan x = sec x

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

A: Given information is :

Q: Compute sin x et + 3e-x

A: