Show that the following holds true. 1 csc A = sec A = cot A = sin A cos A tan A sin A = cos A tan A = cse A sec A cot A

Q: If x=tan , then dr = coso de by trigonometric substitution. (1+x*)½" A True B False

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Q: Q:Prove the following identities: (i) cos A, cos A = sin*A, sin'A (ii) cot A,1=cosec*A , 2 cosec?A

A: There is a sign mistake Right questions are  (1) cos^4A-cos^2A= sin^4A-sin^2A (2) cot^4A-1=…

Q: If A +B = 90° Prove that tan A tan B+ tan A cot B sin' B = tan A sin A sec B cos A

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Q: Find the exact value of the expressions cos(a + B), sin(a+ B) and tan(a + B) under the following…

A: From the given  Sin( α) = 40/41 and Sin(β) = 15/17  Sin(α+β), Cos(α+β),and Tan(α+β) can be…

Q: II. Verify the following trigonometric identities. 7. cot e = 1 tan 0 csc e 8. tan? x = csc² x tan?…

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Q: h a Based on the figure given, which of the following is false? O a. sin(01) sec(02) = 1 b. cos(01)…

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Q: Which of the following is FALSE? 01+ tan? x = sec? æ 1 sec x = CSC x O cot x sin x= cos x = COS X O…

A: Solution ) We know that  1) 1 + tan2x = sec2x 2)Sec x = 1/ cosx 3)Cotx sinx     [ cotx = cosx/sinx]…

Q: 4 tan a = < a < t; cos ß = 7,0<B< 3' 2 %3D a) sin (a + B) (b) cos (a + B) (c) sin (a – B) (d) tan (a…

A: Solution:-

Q: 6. 2/10 2.

A: Solved below...

Q: Which of the following is equal to cos A cos B? 1 [A] [sin(4 + B) – sin(A – B)] 1 [B] [sin(A + B) +…

A: Use trigonometric identities.

Q: (a) cos(a + B) (b) sin(B al =

A: We will find the  required value

Q: Show that the functions f and g are identically equal.

A: Any two functions are said to be identical if they are equal throughout their domain. The tangent…

Q: (a) Show the following identity: cos e 1+ sin e 2 sec 0 + 1+sin 0 cos e

A: Consider the given: Hello. Since your question has multiple parts, we will solve first question for…

Q: tan A - sec A = sin A-1 cos A 2 sin A- cos A cos A O cos A-1 cos A

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Q: Prove the following useful trigonometric identities: (a) cos(a + 3) = cos(a) cos(3) - sin(a) sin(3)…

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Q: QUESTION 2 | sint cos't sec ( cos't ]dt =? Find the correct answer: O a. No correct answer tan (…

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Q: If cos t = – and t is in the 3rd quadrant, then sin t V45 7 V45 7 /53 7 V45 2 V45 2

A: We have to find the value of sin t if t is in third quadrant and cos t=-27. We know the identity,…

Q: Verify the following identities: a. Sin a tan a + cos a = sec a b. tan b + cot b = 2 csc (2b)

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Q: Find sin(a) and cos(B), tan(a) and cot(B), and sec(a) and csc(B). 3 (a) sin(a) and cos(ß) (b) tan(a)…

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Q: that the left hand side of the equation is equivalent the right hand side. Cos a csc z = cot?z tan…

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Q: Which of the following relationships is true? Select one: a. sec A cot A = 1 O b. sin A+ cosec A = 1…

A: The objective of the question is choose the correct relationship.

Q: 5. Verify the following identities. sin(A+ B) cos A cos B a. = tan A + tan B b. sin = cos 0 sin 6 с.…

A:

Q: 1. Simplify the expression cos z(sec a- cos z). COB C O cos? a O sin? a sin T

A: use trigonometric function properties

Q: Find sin(a) and cos(ß), tan(a) and cot(B), and sec(a) and csc(B). 4 7

A:

Q: Find sin(a) and cos(B), tan(a) and cot(B), and sec(a) and csc(B). 20 35 B (a) sin(a) and cos(ß) (b)…

A: Given, Using Pythagoras theorem,

Q: Match the equivalent expressions. O 1- sin?(0) a. cscʻ(0) O sec?(0) – 1 b. tan (0) - O 1- cos (0) c.…

A: The objective is to match the equivalent expressions.

Q: Verify the identity. cot2(t) - cos?(t) = cot2(t) cos?(t) cot?(t) - cos (t) = - cos?(t) sin (t) 1 =…

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Q: Which of the following statements is always true? a. Sin(A) = Cos(A) A b. Tan(B) = Sin(C) c. Cos(B)…

A: A right triangle ABC is given whose angle C is 90o . We have also given four statements, from this…

Q: Q:Prove the following identities: (i) cos*A.cos A = sin*A, sin'A (ii) cot'A ,1=cosec*A,2 cosec?A

A:

Q: Which of the following is equivalent to csc B(sec B– 1)(sec ß+1) for all values of ß for which csc?…

A: Topic = Trigonometry

Q: sec a csc a-2 tan a cos a-sin a cos a+sin a sin a cos a

A:

Q: tan A - sec A = %3D sin A-1 cos A 2 sin A- cos A cos A O cos A-1 cos A

A:

Q: Find sin(a), given that cos(a) = 2/5 and sin(a) < 0.

A: As we know that, the trigonometric identity: sin2θ+cos2θ=1 Given: cosa=25

Q: cosec A/sec A = ? Select one: O a. sin A + cos A O b. tan A O C. cot A O d. cos A

A: Select one

Q: Verify the following identities. (sin x + cos x) = 1+sin 2x а. b. sec? x•tan? x + sec? x = sec* x 2x…

A: Given, The identities  a sinx+cosx2=1+sin2x b sec2x.tan2x+sec2x = sec4x We have to verify the…

Q: Question Which of the following is equivalent to sin 0 cos 0 sec 0 cot 0 for all values of 0 for…

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Q: Use the given sum or difference identity to find sin(a + B) exactly, given that cos a = such that 6.…

A:

Q: 9. Complete the statement below. cos (a+ B) = cos a cos B sin a sin B cos (a+ B)= cos a cos B (1).…

A:

Q: If cos t =- and t is in the 3rd quadrant, then sin t = V45 O V53 V45 V45 V45

A: In third quarternt sine and cosine both are nagetive.

Q: If A +B = 90° %3D Prove that tan A tan B + tan A cot B sin' B = tan A sin A sec B cos A

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Q: (a) sin a = %3D (b) cos a = (c) csc a = (d) sec a = (e) cot a =

A:

Q: Find the exact value of cos(A- B) under the given conditions: [ 4 sin A = V5 Зп TT < A « 2. ta 5 TR…

A: We have

Q: s).F ecosa sin a da cos a sin a da 2

A:

Q: Find the following. (a) sin t (b) cos t (c) tan t (d) sec t

A: It is known that in a unit circle, x2+y2=1 where r=1. It is given that the y coordinate is 2425.…

Q: Given that sin(a)=-3/5 and tan(a)>0, determine the following a.) cos(a) b.) tan (a) c.) sec(a) d.)…

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Q: Use the given sum or difference identity to find sin(a + B) exactly, given that sin a = such that a…

A: Sin2A+cos2B =1

Q: a) Use the formulas  sin(A + B) and sin(A - B) for toshow that sin A cos B = 1/2 [sin(A - B)+ sin(A…

A: a) Use the formulas  sin(A + B) and sin(A - B) for toshow that sin A cos B = 1/2 [sin(A - B)+ sin(A…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.