In Exercises 35–38, find the exact value of the following under the given conditions: a. sin(a + B) b. cos(a – B) c. tan(a + B) d. sin 2a B e. cos 35. sin a = ,0 < a <5, and sin ß = . < B < a. 36. tan a = §. 7 < a < , and tan ß = . 0 < B < }. -3,< a < T, and cot ß = -3,

Q: 7. Evaluate sin(cos-¹(3))

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Q: 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…

A: 6. We have to verify the identity cosx cscx = cotx   As we know, cscx=1sinx and cotx=cosxsinx

Q: In Exercises 63–72, use a right triangle to write each expression as an algebraic expression. Assume…

A: As there are multiple questions 63) is solved here.

Q: What is the exact value of tan{esc^ '(-)),

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Q: VI. Find the exact value of the expresssion: a) cos(sin=1) b) tan(sin¬'#)

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Q: if sin(A)=3/5 A is in QII and tan(B)=7/24 B is in Q3 then determine tan(A+B) and cot(A+B)

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Q: In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of 0. 23.…

A: cos θ = -35, θ in quadrant III sin2 θ + cos2 θ = 1sin2 θ = 1 - cos2 θsin θ = 1 - cos2 θsin θ = 1 -…

Q: cot(-0)+tan(0-) TT = 1 – 2sin² (0) tan(-0)+cot(-0) |

A: The given statement is: cotπ2-θ+tanθ-π2tan(-θ)+cot(-θ)=1-2sin2θ

Q: Evaluate the expression tan cos 8 18 + tan 8 ¹()) . Give an exact answer.

A:

Q: 14) sin- 1 2 /-

A: 14. let x=sin-1(12)     x=π6                    (∵ sin(π6) = 12)

Q: Prove the following identity : 2(sin'q +cos'a) -3(sin'q +cos'a) +

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Q: Verify the identity : cos(α - β)/(cos α .sin β) = tan α + cot β

A: Given : cosα - βcosα sinβ = tanα + cotβ

Q: Which statement must be true? A cos(A) = sin(A) B cos(A) = sin(B) C cos(A) = cos(B) D sin(A) =…

A: for the right angle triangle, let the angle A=x C=90 for triangle sum of all 3 angles is 180…

Q: 3) sin [Arccos (-1)] 2,

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Q: expand the formula for sin(A+B)

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Q: Let x= 2 tan theta, 0 less than or equal to theta < pi/2  simplify the expression  1/x^2…

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Q: Find the values in Exercises 9–11. 9. sin(cos-1(sqrt(2)/2)) 10. sec(cos-1( 1/2)). 11. tan(sin-1(-1/…

A: Find the value of

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

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Q: Sin-1 e こ? 1ーx2

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Q: C) Show that 1 tan 0+cose =sin.20

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Q: 25) n S sin (+) n s

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Q: Which is an appropriate first step in verifying this trig equation? cotx (cotx + tan x) = csc²x %3D…

A: The given Trigonometric identity is,                cotx(cotx+tanx) = csc2x One of the basic…

Q: 11) Prove each identity: a) cos(a+b) cos(a)cos (b) b) 2 sec2(t)= - 1 tan(a) tan (b) 1-sin(t) cos²(t)…

A: a.cos(a)cos(b)cos(a+b)​=1−tan(a)tan(b)Note: For tan(a)tan(b), we have the trigonometric identity…