Let sin A = 4/5 with A in QII and sin B = − 8/17 with B in QIII. Find sin(A + B), cos(A + B), and tan(A + B).

Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

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Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

Q: Given that the sin x = 2/5 and cos x = -1/4 with sin x in Q1 and cos x in Q3, find sin( sin x - cos…

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Q: To begin evaluating S sin*(x) · cos³(x)dx, express a. sin*x to (sin²x)²and use the identity sin²x…

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Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: Find sin 2x, cos 2x, and tan2x if tanx = and x terminates in guadrant II. sin 2x ? cos 2.x tan 2x…

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Q: Evaluate sin (; - i In v2) cos(; - i In i ln v2) i In /2) cos o (3/4)i o (3/8)i o 5/8 o 5/4

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Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: x sin (x²) cos(x²), from a = 0 to b = x 2

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Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: Let sin 0 = with A in QIV. Find the exact value of cos 20 %3D 315

A: A is in QIV. There cos is positive  So,

Q: cos 2x +1 Prove that sin 2x

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: Find sin2x, cos2x, and tan 2x if cosx - and x terminates in guadrant III. 13 sin 2x cos 2x tan 2x

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: Let a > 1 be a constant and y = (9e- sin z 3) In(x+a). Find y'(0).

A: Product rule of differentiation:…

Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

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Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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Q: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: find the exact value of the expressoion:   cos[sin-1(1/2)]

A: We have to evaluate the value of

Q: 4) Find when y? – x² + cos(x + y) = 0

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Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

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Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

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Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: integrate cos^2(t)*sin^2(t) from 0 to 1

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Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant III. V13

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Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

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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 : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Find cos (0 + p) given that cos 0 = and cos p = and that 0 and p are %3D between 0 and n/2.

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Q: O Find the solutions of : 1+sinx=2(cosx)´ in the interval 0<x<2T.

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Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

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Q: Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(C

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