24. Prove the identity sec(x) (sin(x) + cos(x)) sec(x) + 2 sin(x)

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

A:

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

A:

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

A:

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: 5 cos2(x) sin(2x) dx

A:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: 3- cos nX Sin ux dx

A:

Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

A:

Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

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

A:

Q: Establish the identity. sin x+ sin y X+y = tan COS X+ COs y 2.

A:

Q: * Prove: sin x = cos COS 2- 2cos x

A:

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

A:

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: 21. cos x cos 2x + sin x sin 2x

A:

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: - 3in 2 X sin X- COSX

A:

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: cos 2x+1 sin 2.x 7. Prove that sin 2x 1-cos 2x

A: The trigonometric of an acute angle in a right triangle express the relationship between the angle…

Q: provethat 2. 1- cosx +Sin'x

A:

Q: ,(xsinx+cos.x)x'cos"x - x sinx + cos.r cos³ 3 dx x°cos?x

A:

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

A:

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

A:

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: 1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

A: To prove:-

Q: 2. If sin x cos x + sin 2x =1 what are the values of x

A:

Q: 2 tan(2x) − 4 cos(x) = 0

A: Explanation of the solution is given below.... And solve the given equation.....

Q: y = cos (tan (3x)) A. -9cos? (tan (3x))sin (tan (3x)) sec (x) B. -9cos? (tan (3x))sin (tan (x))…

A:

Q: when

A:

Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: Show that n/2 sin x dx sin x + coS X %3D 4

A:

Q: */2 2 cosx dx 1+ (sin x)2 -n/2

A:

Q: |(1+ sin x)'cos x in x) cos x cOS.

A: Given: ∫1+sinx3cosxdx

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment