Prove the following identities sinθ+cotθcosθ=cscθ sinθ(cscθ-sinθ)=cos2θ

Q: Evaluate the following expressions. - sin cos %3D

A: Given that: 1. sincos-1-322. tancos-1-22

Q: Verify the Identity: sin(pi/2 +x)=cosx

A: Since, sina+b=sinacosb+cosasinb Then, LHS- sinπ2+x=sinπ2cosx+cosπ2sinx=cosx where a=π2,b=x

Q: prove the identity of sin(pi/2+)=cosx

A: We know the identity,

Q: Prove the following identity: Sec/cos - tan/cot = 1

A: Prove the following identity secxcosx-tanxcotx=1

Q: Find the algebraic expression in x of: cot (cos" (-)) –

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Q: Evaluate the following so that no trigonometric functions remain: cos ( tan'

A: Consider the given trigonometric function. costan-11x The objective of the problem is to evaluate…

Q: Use the fundamental identity to write two functions for cos a in terms of sin a. Indicate which…

A: The fundamental trigonometric identities can be listed as follows. Pythagorean Identity Reciprocal…

Q: Prove the following identities.         sin theta tan theta + cos theta = sec theta

A: We have to prove: sinθtanθ+cosθ=secθ We know following relations for trigonometric ratios:…

Q: Establish the identity. sin (a + B) = tan a + tan B cos a cos

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Q: Prove that each of the following identities is true.     tan theta cosec theta cos theta = 1

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Q: Prove the following Trigonometric Identity sec(x) – cos(x) sec(x) - sin (x)

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Q: Find the following special values: sin 0 (5) cos sin 6 (6) sin 3 COS (7) sin 7 sin - (8) (27) cos ||…

A: These angles are all standard angles and hence referring to the table of trigonometric ratios all…

Q: Verify the identity sin (a B) = tan a cot ß - 1 cos a sin B

A: To verify the provided trigonometric identity which is show below,

Q: Prove the following identities.         cos theta tan theta = sin theta

A: We have to prove the identity: cosθtanθ=sinθ We know that tanθ=sinθcosθ

Q: Prove that each of the following identities is true.   tan theta  - cot theta = sin 2  theta - cos 2…

A: To prove: tan θ-cot θ=sin2θ-cos2θsin θ cos θ

Q: Prove that each of the following identities is true.   sec theta  - cosec theta = sin   theta - cos…

A: Given identity is: secθ-cosecθ=sinθ-cosθsinθcosθ Since, sinθ and cosecθ are reciprocal to each…

Q: Prove the identity: 1 + tan e= tan e sin cos0

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Q: Verify the following identity. sin(a + B) cos(a)cos(8) tan(a) + tan(B) Work out on your scratch…

A: In this question we need to verify the given identity. We take LHS of the given identity and show…

Q: Determine the exact value of the following: tan () – sin () cot ()

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Q: Prove the following identity: 1) cotθ = cosθ cscθ

A: topic - trigonometric identities

Q: Find the values in

A: Given:

Q: Find the exact value of cos(A+B) if sin A = with A in QI and sin B 5 with B in QID = -

A: Given: sinA=35sinB=-513 To find the exact value of cos(A+B) COS(A+B)=COSACOSB-SINASINB COS2θ+SIN2θ=1

Q: Prove the following identity : sin (x) + cos (x) cot (x) = csc (x)

A: Before solving remember the following relations:

Q: Let cos A = 2/√5 with A in QI and find sin(2A)=

A: In Q1 , sin is positive  So,

Q: Photo is attached

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Q: sin 4t-sin 2t tan t cos4t-cos 2t 5.

A: I am attaching image so that you understand each and every step.

Q: Verify the following identities: sin 20 – tan 0 tan 0 cos 20

A: Solved below

Q: sin (3pi/2 + theta) = -cos (theta)

A:

Q: Prove the following identities.         ( 1+ sin theta ) ( 1 - sin theta  ) = cos 2 theta

A: To Prove: 1-sin θ1+sin θ=cos2 θ Consider Left Hand Side- 1-sin θ1+sin θ= 11+sin θ-sin θ1+sin θ=1+sin…

Q: cos s e + cscOsind| 2. sin²e

A: To simplify cos2θsin2θ+cscθsinθ

Q: Verify the following identities: cot(x) + tan(x) = sec (x) · csc (x) а.

A: Take any random value of x and solve left hand side and right hand side sepretly if both are equal,…

Q: Let a and bbe positive numbers. Evaluate sin (tan (4)) av

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Q: Evaluate the following trigonometric functions exactly if they are defined. Otherwise, write…

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Q: Which of the following is equivalent to sinθcosθsecθcotθ for all values of θ for which…

A: sin θ cos θ sec θ cot θ=sin θ cos θ×1cos θ×cos θsin θ=cos θ

Q: Verify the following identities. a. cscθ - sinθ=cosθcotθ b. (1/sec+1)+(1/sec-1)=2cscθcotθ

A: We have to verify a set of trigonometric identities.

Q: Establish the following identity. cos 0 – cos(30) = tan(20) sin(30) – sin 0

A:

Q: Find the exact value of cos(arctan x)

A: The exact value of cosarctanx=

Q: Prove identity cos ( +a) = - sin

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Q: Let 0 e (7, 27) be' such that tan 0 = . Find sin 0 and cos 0.

A: From the given problem: tanθ=12tan2θ=14sec2θ-1=14sec2θ=54secθ=±521cosθ=±52cosθ=±25  When θ belongs…

Q: Prove that the following identity is true.   sin4 t - cos4 t / sin2 t cos2 t = sec2 t - csc2 t

A: Given that sin4t-cos4tsin2tcos2t=sec2t-cosec2t

Q: Verify the following trigonometric identity:cos4t−cos2t= sin4t−sin2t

A: The trigonometric identities can be verified by solving the left hand side and right hand side…

Q: prove sin(A-B)/cos A cos B=tan A-tan B

A:

Q: You need to find the exact value of tan 12 Which of the following is the correct application of the…

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Q: Verify the identity. sin B + cos B cot B = CSc B %3D

A: Given,           sinB+cosBcotB=cscB

Q: Prove that each of the following identities is true.     cosec theta  tan theta = sec theta

A: cosecθ*tanθ=secθ

Q: following

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Q: Find the right part of the identity. secβ-cosβ=

A: Given,  secβ-cosβ   We have to find the right part of the identity.