If cos a + cos B= a and sina + sin B= b, then show that 2 sin 2a + sin 2B = 2ab 1 a2 + b2

Q: tanθ= 1/2,     π<θ< 3π/2 Find the exact value of cos(2θ)

A: We have to find the value of the given condition

Q: 2 Simplify (sin ½x cos ½x) *

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Q: If sec 0 = -13/6 and sin 0 > 0, what is 3sine + cos(0)?

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Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. 12 cos(x) = 13 csc(x) < 0 sin(2x) =…

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Q: 4 Suppose that sine = and <0<. Find the exact values of cos and tan Cos Undefined tan Continue O

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Q: Verify the identity: 1/(sin θ + cos θ)+1/(sin θ - cos θ) = 2 sin θ/(sin4 θ- cos4 θ)

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Q: / sin*0 d0, factor sin*0 as (sin²o)² sin® and let sin²0 = -(1– cos20). To evaluate A True False

A: Given problem:-

Q: Show that sin ( 40) (cos 0) (4 sin 0 – 8 sin³ 0). %3D

A: To show: That sin 4θ=cos θ4 sin θ-8sin3θ. Formula used: sin A+B=sin A·cos B+sin B·cos A cos…

Q: If cos 2 (5) sin(0) and 0 <0< then 2 0 =

A: cosπ2=sinθ                                L.H.S=cosπ2…

Q: - If 0 = then 3 sin(0) = cos(0) = CoS

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Q: Find cos (20) if sin 0= 8. cos 0>0 17

A: Given : sin θ=817Opposite side to θ is 8hypotenuse is 17 Now use Pythagorean theorem to find the…

Q: Determine the following: (a) sin^−1(√2/2) (b) cos^−1(−1/2) (c) tan^−1(cos(1/2)) (d)…

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Q: Verify the identity 2 sin3θ cos θ + 2 sin θ cos3θ= sin 2θ.

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Q: cos(0)tan(8) sec? (ө) — 1 is written in terms of sin(e) only and simplified, what is the resulting…

A: Topic:- trigonometry

Q: Just tangent

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Q: If csc(x) = 4, for 90° < x < 180°, then CS sin() Cos 2 %3D tan 2 %3D

A: formule: 1. cosec(x) = 1/sin(x) 2. tan(x) = sin(x)/cos(x)

Q: If sin 0 = and 0 <os (a) determine the EXACT value of cos 20 (b) determine the EXACT value of sin().

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Q: Find the exact value of cos(theta/2) given sin theta=-3/5 , where sec(theta)<0

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Q: (a) If cos^2(23∘)−sin^2(23∘)=cos(A∘), then A=   degrees. (b) If cos^2(6x)−sin^2(6x)=cos(B), then…

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Q: Find cos θ and tan θ if sin θ = 0.4 and π/2 ≤ θ &lt; π.

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Q: Show that sin² 0 cos² 0 8 1 cos (40). 8

A: To show that: sin2θcos2θ=18-18cos(4θ) Solution: We know: 2sinxcosx=sin(2x)    ..(1)cos(2x)=1-2sin2x…

Q: True or False sin ( 20) has two equivalent forms: 2 sin 0 cos 0 and sin² 0 – cos 0

A: Given statement is, sin2θ has two equivalent forms: 2sinθcosθ and sin2θ-cos2θ.   The objective is to…

Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

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Q: 3 If sin 0 = -. ,0<0<5, find the exact value of each of the following. 4 2' (a) sin (20) (b) cos…

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Q: 2 sin 510°- cos 340° cos(-20°) | (8) cos 110°

A: I am going to solve the given problem by using some simple trigonometric values to get the required…

Q: Find sin(2θ) if cosθ=− 1/3 and θ is in QII.

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Q: If sin θ =1/4 and 0 ≤ θ ≤π/2 (a) determine the EXACT value of cos2θ (b) determine the EXACT value…

A: Solution

Q: If sin B = B in QI , find with B Cos 3– 2/2 Cos 3 + 3 COS 6 3- 22 6 cos 3 - 212 cos 3 3 + 3 CoS

A: Given that, sinB=13 Find the value of cosB2. We know the trigonometric formula's:…

Q: Verify the identity: 2 sin3 θ cos θ + 2 sin θ cos3 θ = sin 2θ

A: Verify the identity: 2 sin3 θ cos θ + 2 sin θ cos3 θ = sin 2θ

Q: An expression that can be obtained from 4 sin 20 cos 20 + 13 sin 20 cos 20 cos 20

A: Given,            The expression is 4sin2θcos2θ+5cos2θ=13sin2θcos2θ.To find : The another expression…

Q: If it is known that sin 0: and n<0 < find the exact value of cos(20). -

A: Consider the given value. sinθ=-13 The angle lies between third quadrant and the cosine function…

Q: if 0°<θ<90° and sin⁡θ=3/8, find cos⁡2θ.

A: To find: cos2θ Given information: if 0°&lt;θ&lt;90° and sinθ=38 Formula used: cos2θ=1-2sin2θ

Q: If x=5 cos 0 (where 0<0<), then 2 sec 0+5 tan 0 = ...

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Q: Express as a sum or difference.2 sin 9 θ cos 3 θ

A: Given,           2sin9θcos3θ

Q: 12 Determine the exact value of sin 20 given that cos=- and 13 3π 2 π<0< without determining the…

A: Concept: Trigonometric ratios: sinθ=PH; cosθ=BH Where P is perpendicular , H is hypotenuse and B is…

Q: Recall that sin2 0 means (sin 0)². find sin2 0. If sin 0 = sin< 0 =

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Q: (A[cos(6) - 3 cos(3) + 2] + B[– sin(6) +3 sin(3)] = 2, A[sin(6) + 3 sin(3)] + B[cos(6) – 3 cos(3) +…

A: Given that, Acos6-3cos3+2+B-sin6+3sin3sin3k+Asin6-3sin3+Bcos6-3cos3+2cos3k=2sin3k

Q: If cos (2θ) = 3/5 and 0 ≤ θ ≤ π/4, find the values of i. sin (2θ) ii. cos (θ) iii. sin (θ)

A: Given, Cos2θ = 3/5 Formula: Sinθ= √(1-cos2θ) Cos2θ=2cos2θ-1

Q: Find sinθ and cosθ if tanθ=1/5 and sinθ &gt;0.

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Q: Verify the identity. sin 40 = 4 cos '0 sin 0 – 4 sin °0 cos 0

A: To prove that  sin4θ=4 cos3θ sinθ-4sin3θ cosθ

Q: If cos 0+sin 6= /2 cos 0, show that cos 0-sin 6 = /2 sin 6.

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Q: If sec 0 = – and sin 0 > 0, what is 3 sin 0 – cos(-0)? 6-3/133 13 O 6+3V133 13 3/205-6 13 3/205+6 13…

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Q: If sin(0): 3. and 0 is in the 1st quadrant, find the exact value of cos(0) %3D cos(8): %3D

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Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: If tan 0+ tan'0=1, then Find the value of cos*0 + cos 0

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Q: find sin 7x Gs ga da Sin 7oe Cos

A: This question is based on Indefinite Integration.

Q: Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's…

A: This question can be solved using the De Moivre's theorem which says eix=cosx+isinx

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.