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: () V3 е) Cos b) sin'(0) h) tan 13

A: (b) We have to find angle of sin-10. Let θ=sin-10 ⇒sinθ=0 We know that sinx has its value 0 at x=nπ,…

Q: What is sin(A)? 13 |12 A 5 [ ? sin(A) =

A: We can find the value from the law of trigonometric ratio.

Q: For Exercises 3–4, find the LCD of the expressions. 1 cosx sinx sinx 4. cosx' cos?x sinx cosx 3.…

A: Given: 3)  sinxtanx−1; cosxtanx+14)  sinxcosx; 1cos2x; cosxsinx

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: tan x -1 X 1+ x?

A: To evaluate the given

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)

A:

Q: SinA (1+cos A) = 2cosecA (+cos A) sin A

A:

Q: 3 – 5 (cos (a) + cos²(ß)

A: Given: 3-5cos2α+cos2β

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

A:

Q: For Exercises 73–104, verify that the equation is an identity.

A:

Q: Assume a is positive, find cos(tan-) (show your work)

A: Given, x is positive To find cos(tan-1x)

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: 7. Evaluate tan'(sin 5).

A:

Q: Suppose -π/2 <θ < 0 and tan θ= -2 Evaluate (exactly) (a) cosθ (b) sinθ

A:

Q: Given that tan(0) = 1, what is tan(20)?

A: Given that tan(θ)=72Formula: tan(2θ)=2tan(θ)1-tan2(θ)

Q: Sin-1 e こ? 1ーx2

A:

Q: Prove tan x + cos x = sin x (sec x + cot x).

A: We have to prove the identity: tan x+cos x=sin x sec x+cot x We know the relation between…

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

A: