6. sin2e + tan?e + cos2e A. sin 0 C. cos3 e B. sec2 e D. tan2 e Tse the fundamenta1 identities to fnd th ot

Q: 8. S 3+9 tan² 0 sec² 0 de 0+tan3 0 9. [3 cos 0 e sin 0 do

A: Explanation of the answer is as follows

Q: Siven cos x E and π x<. 5 ", find tan(2x) %3D

A:

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

A: Use the trigonometric identities and simplify to prove the given expression. Also check for a value…

Q: 13. Evaluate the function. Give the exact value. cos (tan (V3) -1 cos(arctan( v3% )= 0.5

A: We have to find out the value

Q: Solve the differential equations

A: Concept to  be used - We will be solving this differential equation using Integrating factor.Given…

Q: -(sin^2 θ + cos^2 θ)

A:

Q: Verify the identity. sin 0-1 tan 0- sec 0 %3D cos e

A: Here we use basic identities of trigonometric ratios.

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: 4. sin 20 + cos 0 = 0 on the interval [0, 27) *Hint: use Double Angle Formula

A: sin(2θ)+cos(θ)=0We know that ,…

Q: Prove the identity: cos(x + y)cos(x – y) = cos?x – sin²y

A:

Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: 1 Evaluate: sin'x cos x

A:

Q: Establish the identity. cos e 1 cos 0- sin 0¯ 1- tan 0

A: Given,            cosθcosθ-sinθ=11-tanθ

Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

Q: EX-4- Prove the following identities : a) Csce + tan 0.Sece = Csc0.Sec'e b) Cosʻ0 – Sin´0 = Cos²0 –…

A:

Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

A:

Q: Find of: y = Tan? (sin-1(x*)) %3D

A: Find the derivative

Q: I = cos? x sin x In(cos x)

A:

Q: 元) D let cos x Let and Cosx lies below the x axis Ę Find sin (2x), Cos(2x) and tan (2x).

A:

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

A:

Q: Prove the identity: sin (x-y) tanx- tany cosx cosy

A:

Q: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: 3 sin(0) + 5 cos(0)

A:

Q: 1- sine = sece- tan e %3D CoS cos e

A:

Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: 8) Prove the trigonometric identity. (sin z + cos r)? = 1 + sin (2r)

A:

Q: Verify the identity. 2 cs" e 1-- 1+ sin 0 = sin 0

A:

Q: I sin r cos xdx. 6. Evaluate sin ¹3 3

A:

Q: 15. Evaluate Sin x cosx dx 2x Your answer 16. Evaluate se 3cos 2x Sin 2x dx Your answer

A:

Q: 5. Prove the identity. csc 0- cot 0 sin- 2 2 csc e

A:

Q: Mutiply    (3 sin  theta +4 ) (5 cos theta + 2 )

A:

Q: 23-Frove that. Cos3e - Cos'e- 3 Cos e Sin'e

A:

Q: 4. sin B + cot B cos B = 1 5. cos 2B – 3 sin B +1 = 0 To di ol

A: Solution: (4) Consider the given trigonometric equations is sin β + cot β cos β = 1 we have  cot β =…

Q: 1+ sin 0 cot e Prove : 1- sin 0 (cos ece – 1}

A: Given:                            1+sin θ1-sin θ=cot2θcosec θ-12 Solve left hand side:…

Q: (4) Use diffential equations to prove the trig identity sin(r + a) = sin(r) cos(a) = sin(a) cos(x)…

A: Given: sin(x+a)+sin(x)cos(a)=sin(a)cos(x)

Q: sin 0 cos 0 d0. Jo 0,

A: Here we to solve definite integral.

Q: Verify the trigonometric identity sin(z - 1/2) = - cos(z)

A:

Q: The relations cosh(i t) = cos t and sinh(i t) = i sin t were discussed in the Excursion. Use these…

A:

Q: 6. sin A = cos A tan A

A:

Q: Verify the identity.

A: Given,           The identity is cosθ+sinθtanθ=secθ .

Q: 1 – 3 sin (x) 2 cos (x) dx. (Hint: start by rewriting the integrand function as 3 sin (x) 2 cos (x)…

A:

Q: cos e) tan (0) +3tan(0)=0

A:

Q: Cos O tan 0 66. lim 0→0

A: Consider the given function. limθ→0   cosθtanθθ

Q: cos 2x+sin? x 1.4 a) Prove the identity: =1- sin x. 1+ sin x

A:

Q: 1- cos 0 1+ cos 0 sin 0

A:

Q: (a) cos (tan (1)) = V2 (b) sin cos 2.

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.