(a) Prove that, ifn>1 is a natural number, then tan"(r) dr tan-(r) tan" (4) dr. R-1 Use this formula to evaluate / tan'(z)dz.

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

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

A:

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

A:

Q: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: .2 -If tan -1 = 0, then prove that x2 sin 2 a. %3D

A:

Q: iV. Prove that tan50 t5-10t3+5t where t tan0. Deduce the values of 5t4-10t2+1 tan for n 1,2,3,4.

A: Consider the given information: To prove that tan5θ=t5-10t3+5t5t4-10t2+1,   t=tanθ

Q: Find the root of 1+ tanh x - 2 tan x = 0.

A: We find the root of  1+tanh(x)-2tan(x)=0 , by Newton's method.

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

A:

Q: 2. Find the exact value of sin(a + B) under the given conditions. 5 tan a = 12 코T< a< 프, sin ß = -,…

A:

Q: 4. a. Find the exact value for: tan(5) b. Solve for x: tan(2x) = √3, x€ [₁] 2

A: (a) The objective is to find the exact value for tan5π3. (b) Given equation tan(2x)=3,  x∈-π2,π. The…

Q: 7. What is the exact value of tan (-105°)? O -2 – V3 O 2 - V3 O 2+ v3 O -2+ V3

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: a) Show that sin¯'x + cosx = 2 E) - tan-' (). x(x-y) y(x+y) (b) Find the value of tan1 where >-1…

A: We can solve these two question by using the properties of inverse trigonometric function as below.

Q: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

A:

Q: Prove the trigonometric identity  1+sec2x /over/ 1+tan2x=1+cos2x

A:

Q: (-등, 풍) satisfying TT Find all values of 0 in the interval 2 2 2 the equation (1 – tan 0)(1 + tan 0)…

A:

Q: Prove the identity. cos (x-y) 1+ tanx tany cosx cosy

A: cos(A-B) = cos(A) Cos(B) +sin(A) sin(B)

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: -1 1- x² 1+x? Differentiate cos with respect to tan -1 2x 1- x2 '

A: Derivative of one function with respect to another function. Using substitutions to find derivative.

Q: 3. Prove that the identity is true. sin*t - costt tan-t– 1 cos't

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: 3 Find sin 2x, cos 2x, and tan 2.x if cos.x = and x terminates in quadrant II. V10 sin 2x %3D

A: given

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

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

A:

Q: what is the general solution for -1=2tan(x) + tan2(x)

A: Simple calculation of trigonometric ratio

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: ( 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: II Find sin .2 4), and tan4) from the given in 2. 10 sec(x) = , 270° < x < 360° %3D sin 2 (즐) - %3D…

A:

Q: 1 The linear approximation of tan-6° is? approximation of 3√9 is? 2 The linear

A:

Q: ind sin2x, cos 2x, and tan 2.x if tanx = -2 and x terminates in guadrant II. %3D sin 2x ? cos 2x tan…

A: In second quadrant sin is positive and cos &amp; tan are negative.

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.  sin x = tan x

A:

Q: 1-To find the smallest positive root of tan x-x=0 which of the following re-arrangement is…

A:

Q: Cos (GX) = Cos 15°, 0°<x < 360° Со X) = Cos 15°, O° < x < 360° %3D Tan( x ) = tan,05x < 2n )= tan,

A: We can find the answers as below

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

A:

Q: 7. Verify the identities: tan x tan x tan20 1-cos e a) 1+sec x = 2 csc x b) sec 0+1 %D 1-sec x cos e

A:

Q: 1. Given tanx = - and cos x >0, find secx. A. в. C. V10 D. 2V10 2. Given secx and sin x 0. 3. Find…

A:

Q: 2 and 3 Suppose that tan 0 <0<T. Find the exact values of sin and tan JT sin 2 = Undefined tan 2

A:

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: A tangent reduction formula Prove that for positive integers n + 1, tan"-x п — 1 tan" x dx tan" -2x…

A: To Determine: A tangent reduction formula find the integral ∫0π4tan3xdx Given: we have reduction…

Q: 12. Find the exact simplified function value of tan (2a). 4 where TTSAL 3T 2. Given sin a= -

A:

Q: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

A:

Q: x) - 0.5 cos(x)) on the

A: Given as, f(x)=e-x3.2sinx-0.5cosx in the interval [3, 4].

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Q: 2x,given  tanx=2 and cosx>0

A:

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

A: Consider, tanx-tany=sinxcosx-sinycosy=sinx cosy-cosx sinycosx cosy=sinx-ycosx cosy…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.