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study help
mathematics
precalculus

Questions and Answers of Precalculus

Show that the functions f and g are identically equal.f(x) = sin x ∙ tan x g(x) = sec x - cos x
Establish identity.ln |sec θ + tan θ| + ln |sec θ - tan θ| = 0
Establish identity.ln |1+ cos θ| + In |1 - cos θ| = 2 ln |sin θ|
Establish identity.ln |tan θ| = ln |sin θ| - In |an θ|
Establish identity.ln |sec θ| = -ln |cos θ|
Establish identity.(sin α - cos β)2 + (cos β + sin α)(cos β - sin α) = -2 cos β (sin α - cos β)
Establish identity.(sin α + cos β)2 + (cos β + sin α)(cos β - sin α) = 2 cos β (sin α + cos β)
Establish identity.(tan α + tan β)(1 - cot α cot β) + (cot α + cot β)(1 - tan α tan β) = 0
Establish identity. tan a + tan B cot a + cot B tan a tan B
Establish identity.(2a sin θ cos θ)2 + a2 (cos2 θ - sin2 θ) 2 = a2
Establish identity.(a sin θ + b cos θ)2 + (a cos θ - b sin θ)2 = a2 + b2
Establish identity. + cos 0 + sin 0 sec e + tan e 1 + cos 0 – sin 0
Establish identity. 1 + sin 0 + cos 0 1 + sin 0 – cos 0 1 + cos 0 sin 0
Establish identity. 1 - 2 cos? 0 sin 0 cos 0 = tan 0 – cot 0
Establish identity. (2 cos? e – 1)? cos e – sin* 0 = 1 – 2 sin? e
Establish identity. cos 0 + sin 0 – sin³ 0 sin 0 cot 0 + cos? 0
Establish identity. cos? 0 – sin? 0 1 - tan? 0 cos? 0
Establish identity. sin3 0 + cos? 0 1 - 2 cos? 0 sec 0 - sin 0 tan 0 – 1 CoS
In Problems, establish each identity. sin' e + cos' 0 1- sin 0 cos 0 sin 0 + cos 0
In Problems, establish each identity. sin 0 + cos 0 sin 0 - cos 0 sec 0 csc cos 0 sin 0
In Problems, establish each identity. sin 0 + cos 0 cos 0 - sin 0 sec 0 csc 0 sin 0 cos e
In Problems, establish each identity. sec v tan v + tan v sin v + cos v sec v
In Problems, establish each identity. (sec v – tan v)? + 1 = 2 tan v csc v(sec v tan v)
In Problems, establish each identity. 1 + sin 0 (sec 0 + tan 0)² 1 - sin 0
In Problems, establish each identity. 1 + sin 0 cos 0 sec e 1- sin 0
Establish identity.
Establish identity.
Establish identity.tan θ + cot θ = sec θ csc θ
Establish identity.sec θ - cos θ = sin θ tan θ
Establish identity. sin? 0 – tan 0 cos“ 0 - cot 0 tan? 0
Establish identity. sec 0 - csc 0 sec 0 csc 0 sin 0 - cos 0 cos 0
Establish identity. 1 - cot? 0 1 + cot? 0 + 2 cos? 0 = 1
Establish identity. |1 – tan? 0 tan 0 + 1 = 2 cos? 0 1 + tan? 0
Establish identity. sec 0 cos 0 1 + sec 0 sin² 0
Establish identity. sec 0 + tan 0 cot 0 + cos 0 tan 0 sec 6
Establish identity. tan u – cot u tan u + cot u + 2 cos? u = 1 %3D
Establish identity. tan u tan u + cot u cot u + 1 = 2 sin? u
Establish identity. sin? 0 1 + cos? 0 sec e – cos 0 sec 0 + cos 0
Establish identity. tan 0 – cot 0 sin? 0 – cos? 0 cot 0 CoS tan 0 + cot 0
Establish identity. sin 0 – cos 0 + 1 sin 0 + cos 0 – 1 sin 0 + 1 cos 0
Establish identity. tan 0 + sec 0 – 1 tan 0 – sec 0 + 1 tan 0 + sec 0
Establish identity. sin 0 cos 0 cos“ 0 - sin? 0 tan 0 1 - tan? 0
Establish identity. tan 0 + cos e 1 + sin 0 = sec 0
Establish identity. tan 0 1 - cot 0 1 - tan 0 1 + tan 0 + cot 0 cot 0
Establish identity. cos e 1 - tan 0 sin e 1 - cot 0 sin 0 + cos 0 cot 0
Establish identity. 1 - cos 0 1 + cos 0 (csc 0 – cot 0)?
Establish identity. 1 - sin 0 1 + sin 0 (sec 0 – tan 0)²
Establish identity. sin? 0 1 + cos 0 cos e
Establish identity. sin 0 sin 0 – cos 0 1 - cot 0 ||
Establish identity. 1 + sin v 2 sec v 1 + sin v cos v
Establish identity. 1 - sin v 2 sec v cos v 1 - sin v cos v
Establish identity. cos e + 1 1 + sec 0 1- sec 0 cos e – 1
Establish identity. 1 + sin 0 1 - sin 0 csc e + 1 csc 0 - 1
Establish identity. csc e – 1 cot 0 csc e + 1 cot 0
Establish identity. sin 0 sec e 2 tan 0 csc e cos e
Establish identity. 1 - sin v 1 + sin v csc v – 1 csc v + 1
Establish identity. 1 + tan v 1 - tan v cot v + 1 cot v – 1 ||
Establish identity. sin? 0 1 1 - -cos e - cos 0 cos e ||
Establish identity. cos? 0 1 + sin 0 sin 0
Establish identity.9 sec2 θ - 5 tan2 θ = 5 + 4 sec2 θ
Establish identity.3 sin2 θ + 4 cos2 θ = 3 + cos2 θ
Establish identity. sin u 1 + cos u cot u csc u
Establish identity. tan u 1 + sin u sec u
Establish identity.csc4 θ - csc2 - cot4 θ + cot2 θ
Establish identity.see4 θ - sec2θ = tan4 θ + tan2 θ
Establish identity.tan2 θ cos2 θ + cot2 θ sin2 θ = 1
Establish identity.(sin θ + cos θ)2 + (sin θ - cos θ)2 = 2
Establish identity.(1 - cos2 θ)(1 + cot2 θ) = 1
Establish identity.cos2 θ (1 + tan2 θ) = 1
Establish identity.(csc θ + cot θ)(csc θ - cot θ) = 1
Establish identity.(sec θ + tan θ)(sec θ - tan θ) = 1
Establish identity.(csc θ - 1)(csc θ + 1) = cot2 θ
Establish identity.(sec θ - 1)(sec θ + 1) = tan2 θ
Establish identity.sin u csc u - cos2 u = sin2 u
Establish identity.tan u cot u - cos2 u = sin2 u
Establish identity.sin θ (cot θ + tan θ) = sec θ
Establish identity.cos θ (tan θ + cot θ) = csc θ
Establish identity.1 + cot2(-θ) = csc2θ
Establish identity.1 + tan2(-θ) = sec2 θ
Establish identity.sec θ ∙ sin θ = tan θ
Establish identity.csc θ ∙ cosθ = cot θ
Factor and simplify:Simplify trigonometric expression by following the indicated direction. cos 0 – 1 cos? 0 cos e Cos
Factor and simplify:Simplify trigonometric expression by following the indicated direction. 3 sin? 0 + 4 sin 0 + 1 sin? 0 + 2 sin 0 + 1
Multiply and simplify:Simplify trigonometric expression by following the indicated direction. 0 + 1) – sec² 0 (tan 0 + 1)(tan tan 0
Multiply and simplify:Simplify trigonometric expression by following the indicated direction. |(sin 0 + cos 0)(sin 0 + cos 0) – 1 sin 0 cos 0
Rewrite over a common denominator:Simplify trigonometric expression by following the indicated direction. 1 + cos v 1 - cos v
Rewrite over a common denominator:Simplify trigonometric expression by following the indicated direction. sin 0 + cos 0 cos 0 – sin 0 sin 0 cos 0
Simplify trigonometric expression by following the indicated direction.Multiply 1 - cos 0 by 1 - cos 0 sin 0 1 + cos 0
Simplify trigonometric expression by following the indicated direction.Multiply 1 + sin 0 cos e - by- 1 + sin 0 1 - sin 0
Rewrite in terms of sine and cosine functions:cot θ ∙ sec θSimplify trigonometric expression by following the indicated direction.
Rewrite in terms of sine and cosine functions:tan θ ∙ csc θSimplify trigonometric expression by following the indicated direction.
True or Falsetan θ ∙ cos θ = sin θ for any θ ≈ (2k + 1)π/2.
True or FalseIn establishing an identity, it is often easiest to just multiply both sides by a well-chosen nonzero expression involving the variable.
True or Falsesin(-θ) + sin θ = 0 for any value of θ.
Fill in the blankcos(-θ) - cos θ = __________.
Fill in the blanktan2 θ - sec2 θ = __________.
Suppose that f and g are two functions with the same domain. If f(x) = g(x) for every x in the domain, the equation is called a(n) ________. Otherwise, it is called a(n) _______ equation.
True or Falsesin (-θ) + cos (-θ) = cos θ - sin θ.
True or Falsesin2 θ = 1 - cos2 θ.
(a) Find an approximation to the integral using a Riemann sum with right endpoints and n − 8.(b) Draw a diagram like Figure 3 to illustrate the approximation in part (a).(c) Use Theorem 4 to

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