Find: a) Sin(A + B) b) Cos(A - B) **Do no find tan (A - B) 12 where 0

Q: 10. Find the exact value of cos 2x given that cos x =

A:

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

A:

Q: 7. Find the exact values of: a) sin ¹(1) b) tan-¹(0) 5-¹ (13) 2 COS

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: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: Find sin(2x), cos(2x), and tan(2x) from the given informa 15 tan(x) x in Quadrant II 8 240 sin(2x) =…

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 4 - cos(x) > 0 sin(2x) =…

A: Answer

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: (2) Find the exact value of the following: (i) cos-(-) (ii) tan-V3 (ii) 2tan-1+ tan-1, (iv) sec…

A: (i) cos-1(-1/2) = 2π/3 (ii)tan-1(√3) = π/3

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

A:

Q: a. sin x = x – 1, а. (1,2) - b. In x = tan-1x, (3,4)

A:

Q: If tan then 1– 2 1+ z2 COS X 8 |N

A:

Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

A:

Q: 2. Find the exact value a. sin'' -1/2 b. arccos - с. tan-1(tan - )

A:

Q: (2k + 1). True or False tan 0. cos 0 = sin 0 for any 0 + %3D

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

A:

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: Complete the statements.

A: Given Our aim is to complete the sentence

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

A:

Q: 2. Verify the following identities (a) sec e - tan@ =sec 0+tan6 sec 8+tan 6

A:

Q: find the exact solutions in the interval (0,2pi) tan x/2 - 2sinx = 0

A: the exact solutions in the interval (0,2pi) tan x/2 - 2sinx = 0

Q: 1. Find (a) sin(x + y), (b) cos(x + y), (c) sin(x – y), (d) cos(x – y), (e) quadrant containing x +…

A:

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: y=tanu Differentiating with respect to u, we get dydu=sec2u Now clearly, sec2u≥0 for every value of…

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

A: Simple calculation of trigonometric ratio

Q: sin(플 + 2x) %3D cos(플 - y) 2- Which of the following is the relationship between x and y according…

A:

Q: 3. Find the degree solutions if 0 <x < 360°. tan x - cos x tan x = 0

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

Q: 8. Find all 0 such that -180° <0 < 180° and: cos 0 = - b sin 0 = c tan0 = - a d cos 0 = 0.8 e tan 0…

A: we have given -1800≤θ≤1800a. cosθ=-110⇒θ=cos-1(-110)=95.740b. sinθ=45⇒θ=sin-1(45)=53.130c.…

Q: 5. Solve for the values of sin2x, cos2x and tan2x when tanx = 1, on 0 ≤ x ≤

A: Given that,    tanx=12, on 0≤x≤π2

Q: how many solutions does (tan(x)-4)(cot(x)-2)(5cos(x)-6)(cos(x))=0 have in the interval [0,2pi]

A: Given:

Q: (10) Find the exact values for x in the interval 0,270 that SatisfY the equation 3Sin2x +2…

A: here we first factorize the given equation and find its roots in terms of sinx and cosx and then…

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: 7. Consider the identity _2 tanr 1+tan z sin(2r). (a) Verify the identity. (b) Find sin (4) if tan…

A:

Q: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

A:

Q: find maclurin formula in the fourth degree for f(x)=tanx

A:

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

A:

Q: 24 and cos(x)= 25 7 what is the vaule of tan(x) 25 If sin(x)= ? z,

A: According to the tangent identity, tan(x)=sin(x)cos(x). We know the value of sin(x) and cos(x), so…

Q: (a-B) (at sin (a+B) 2- show that cosa – cosß = -2sin 2.

A:

Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

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: Complete the statements.

A: a). As x→-1+, sin-1x→-π2

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos x= and x terminates in quadrant I. 17 sin 2x cos 2x tan 2x…

A: Given cos x = 1517 and x terminates in quadrant Iwe find Sin 2x , Cos 2x, tan 2xwe know that in…

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: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: What is the exact value of sin ( cos (-)) + tan- (sin (5))? 2/2-a 4 -2v2+x 2/2+ -2V2-n 4.

A:

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

A:

Q: 2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f)…

A: (a) Consider the given expression: sin-1-1 Sine gives negative one as it value at -π2. Therefore,…

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.