In Exercises 6–11, verify each identity. sec x 6. cos x csc x = cot x 7. cot x + tan x sin x cos x 1 + sin x 8. 1- = sin x 9. cos e + = -sin e sin(a - B) 10. sin a cos B 1 - cot a tan B 11. sin t cos t(tan i + cot t) = 1

Q: Verify that the equation is an identity. 2 sin x tan 2.r = 2 cos x - sec x

A:

Q: Verify the identity. csc(x) cos²(x) + sin(x) = = = csc(x) cos²(x) + sin(x) = csc(x) 1 sin(x) 1 2…

A: Given csc(x)cos2(x)+sin(x)=csc(x)

Q: 2 sin*x · cos³x dx

A: To evaluate ∫0π2 sin4x . cos3x dx using WALLIS formula.

Q: Prove the identity cot (x)+tan n(x)%3Dsec(x)csc (x)

A:

Q: 2. If tan x = Find the sin x and cos x in the interval xe [n. : XE T,

A:

Q: Evaluate : 1) | cos x 3) [ cos x 2) [ ,cot ydy sin' x 1+ sin x 7/4

A:

Q: 1. Explain the steps in verifying that the following equation is an identity. cos x sec x + tan x =…

A:

Q: In Exercises 17-26, use an addition or subtraction formula to find the exact value. 17. sin- 12 18.…

A: Given 1)sin(7π12) 2) cos(105)We need to find the value using addition or subtraction formula

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: Establish the identity. sin x+ sin y X+y = tan COS X+ COs y 2.

A:

Q: Establish the identity. cos e 1 cos 0- sin 0¯ 1- tan 0

A: Given,            cosθcosθ-sinθ=11-tanθ

Q: Match the equivalent expression 1. 2. 3. 4. 5. 6. 7. csc0 tan 0 sin² 0 sece 1 + tan²0 1 + cot² 0…

A:

Q: 7) Verify the identity (cot x – csc x)(cos x + 1) = -sin x

A:

Q: 1. Prove the given identity Isio cot x tanx cosX CotX + tanX

A:

Q: In Exercises 25–28, sin t and cos t are given. Use identities to find tan 1, csc t, sec t, and cot…

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: Evaluate using Wallis' Formula: So sin® x cos4 x dx -Tt/2

A:

Q: Complete the identity. sin 2x- tan x = ? O A. tan x cos X O B. - tanx cos 2x O C. tan x cos 2x O D.…

A:

Q: Verify the identity: sin (x + π/2) = cos x

A: We have to verify the identity sinx+π2=cosx We know that sina+b=sina cosb+cosa sinb Using the…

Q: Verify the identity. 2 sin(x) cos(x) = 1 (sin(x) + cos(x))2 - 1

A:

Q: For Exercises 47-52, verify that the equation is an identity. (See Example 6) sine cos 0 47. csc 0 -…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

A:

Q: 18. Which expression is equal to + tan x using identities? tan r 1 sin z cos x sin x cos x sin a Cos…

A: Which expression is equal to??

Q: Simplify. 1+ sin 2x+ cos 2x COS X O A. 2(sinx+ cos x) O B. 2 tan x O C. 2 cot x O D. 2(sin x- cos x)

A: We have to silmplify

Q: In Exercises 35–38, find the exact value of the following under the given conditions: a. sin(a + B)…

A: The given expressions are trigonometric functions; hence, trigonometric function properties help to…

Q: Question in image.

A:

Q: 1 Prove that sin x tan x = cos x. cosx

A:

Q: Evaluate using Wallis' Formula: 7 sin? x cos5 x dx

A: follow next step

Q: Find sin x/2, cos x/2, and tan x/2 from the given information. cos(x) = − 12/13 ,   180° < x < 270°

A: Given

Q: (5) Verify the following identities.(a) cot x + tan x = sec x csc x(b) sec4 x − sec2 x = tan4 x +…

A: (a) The given trigonometric identity is,

Q: 9. Verify the identity. (1–cos² x)(csc x) cot x 2 sin x(tan x) a)a

A:

Q: Prove the following identities 1. (cot x − csc x)(cos x + 1) = − sin x 2. sin 3x + sin 7x/cos 3x −…

A: 1. (cot(x) - cosec(x))(cos(x) + 1) = -sin(x)   Taking LHS, = (cot(x) - cosec(x))(cos(x) + 1) =…

Q: prove the identity  sin(x) + sin(3x) = 4 sin(x) cos2(x)

A:

Q: Which expression is equivalent to O cotx+sec x O cos x + cot a Otan x+sec x O sinx+tan x an £ ? cos…

A:

Q: In Exercises 7–12, one of sin x, cos x, and tan x is given. Find the other two if x lies in the…

A: Note: Hi there! Thank you for the question, as per our honor code, we have the right to solve only…

Q: T 29. sin x -Cos x

A:

Q: Verify the identity. 1- sin 0 cos e cos 0 1- sin 0 =2 sec e To verify the identity, start with the…

A: We can verify the identity as below using trigonometric formulas.

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

Q: Find the values in Exercises 9–12. 9. sin(cos "() (E-). (ar (-) (cur ) 10. sec( cos 2 /3 11. tan (…

A:

Q: 4. Verify the'following identity. csc x – tan = cot x

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: In Exercises 19–24, assume that 0 < 0 <T/2. 19. Find sin 0 and tan 0 if cos 0 5 13

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 7. Verify the identities: tan x tan x tan20 1-cos e a) 1+sec x = 2 csc x b) sec 0+1 %D 1-sec x cos e

A:

Q: Match the equivalent expressions. o tan(x) O cot(x) o sec (x) O 1– cos (x) a. sin"(x) + cos (x) b.…

A: topic - trigonometric identities

Q: and tan (x) < 0, use the fundamental identities to determine sin (x) = cos (x) = tan (x) = cot (x) =…

A: Given query is to find the value of trigonometric functions.

Q: Use the fundamental identities to match equivalent expressions. cos(0) + 1 tan(0) 1 а. cos(0) – 1…

A: Required solution for above questions are given below ;

Q: Verify the identity. (Simplify at each step.) cos t seci cos t sec(플-)- (cos: 1 = (cos t) cos t =…

A: We have to verify he identity  cost⋅secπ2−t=cott We know that secπ2−t=csct Hence,…

Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

A:

Q: Verify the identity: sin t tan t = (1 - cos2 t)/cos t

A: To Prove - sint tant = 1-cos2tcost