prove it 9. sinx cotx + cosx tan?x = 1 10. (tan x + cot x) = csc?x sec²x sin 2x 11. 1+ cos 2x = tan x cos(x + y) 12. cot y - tan x cos x sin y

Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ sec?x sin?x = sec?x

A:

Q: 6(cos² x – 1) x – 1) sin x cos a – sin z O 6 tanx + 6 sec z O 6 cot x+ 6 sec x O 6 tanx + 6 csc z O…

A:

Q: 2 Using the relation 2 (1 cosx) x, V x € (0, - · 4)

A: A relation is given by, 21-cosx < x2, where x≠0. The objective is to use the given relation to…

Q: 1. y = 3 sin x – 4 cos x 2. y = x³ tan x 3. f(x) = cos x 1+sinx 4. y = csc x cot x f(x) cin?

A:

Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

A:

Q: 1. sin (5x + ) sin ( x + T /2) %3D 2. tan (3x – T/2 ) = cot 2x 3. COs (x + п /2) sin ( T /2 – 2x )…

A: Given that three trigonometry equation  To find fundamental solution of the question

Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: he interval [0,2r) cos (x) sin (x) = 2 cos (x)

A:

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

A:

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: Prove: sin x tan x+cos xcot x+2 sin x cos x = tan x+ cot x + cos²

A:

Q: 2. tan x csc x + cot x sin x = sec x + cos x

A: As you mentioned question no 2 solved

Q: 1/sin(x)/cos (x)+cos (x)/1+sin(x)=4 Prove

A: For x= pi/3

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: Prove the identity. tan(x -)- -cot(x) TC tan x 2 %3D sin(x - ) | tar(x-)- sin(x) cos) - cos(x) sin…

A:

Q: sin 2x+cos2x+1 1- Prove cot x sin 2x-cos 2x+1 2- Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: Evaluate the following 1-prove sin 2x+cos 2x+1/sin 2x-cos 2x+1=cot x 2-sinh(u-v) = sinh u.cosh v-…

Q: 4. Prove the identity: sin x + tan x = tan x cos x + 1 (sinx¥, sin x COS X LS = cosx + 1 V sin x cos…

A:

Q: If y = f (x) = In (cosx), then, f' (x) =? O tan (x) O-sinx (x) -tan (x) O-cot (x)

A:

Q: 2. The cancellation property sin (sin x) = x is valid for x in the interval Which of the following…

A: (i) Consider the provided information, sin-1sinπ3=π3 Prove that left hand side is equal to right…

Q: Prove the identity. sin(2x) 1+ cos(2x) tan(x) = 2 sin(x) · sin(2x) 1+ cos(2x) 1+ (2 cos?(x) – 1) 2…

A:

Q: – 1) sin a cos a - sin æ 9(cos² e – 1) O 9 tanx + 9 sec a O 9 cot a + 9 cscx O 9 tana + 9 csc a O 9…

A:

Q: What is the value of 4 (sin x tan dx X)? a) sin x + tan x sec x b) cos x + tan x sec x C) sin x +…

A: ddxsinxtanx= cosxtanx+sinxsec2x=sinx+tanxsecx

Q: Find the limits in Exercises 36-40  Are the functions continuous at the point being approached?

A: We’ll answer the first three questions since we answer only one question at a time. Please submit a…

Q: TT True or False tan 0 • cos 0 sin 0 for any 0 # (2k + 1) %3D

A:

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: 9(cos x – 1) sin z cos a – sin a O 9 tan + 9 seca O 9 cotx + 9 csc x O 9 tan + 9 csc z O 9 sin x + 9…

A:

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

A:

Q: 1. cos x 1 - sin x = sec x + tan x

A:

Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

A:

Q: 6(cos² x – 1) sin a cos z – sin z O 6 cot x + 6 sec x O 6 tanz + 6 csc x O 6 sin z + 6 cos a O 6 tan…

A:

Q: Prove that (csc(x)) = -csc(x) cot(x). dx 1 d -(csc(x)) d dx )(0) – - 1 sin2(x) sin?(x) 1 sin(x)…

A:

Q: 41 Prove al tanx + cosx= Sin X (sec x+ Cot x) メ b) Cos 2 ttan' t= Sin? t es Cos? (tan"x+ 1 = 1 %3D

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: cos ax dx = xe", a 2 0. (or) Evaluate x' +1 cos ax 2: Prove that x +1

A:

Q: 4sin'x – 1 1. 2sinx + 1 = 2sinx – 1 sin'x – 2sinx + 1 2. = sinx – 1 sinx – 1 3. ( sinx - cos x)(sinx…

A: Simply use the basic concepts of algebra and simplify the each one.

Q: 4. f(x) = Cos Ex) – 5 Stnh (x) %3D 5. f(x) = Sin(3x)Cos(x) (Hint: use product-to-sum trigonometric…

A:

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: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: 5. Verify the following trig identities: A. secx tan x sin x = cos x B. secy_tany =1 cos y cot y C.…

A: The given query is to prove the following trigonometric identitites: secx-tanxsinx=cosx…

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: JK JM sin x cos x + cos x sin x tan x + cot x = tan x + tan x + cot x = tan x tan? x + 1 sin? x +…

A:

Q: 6(cos² x – 1) sin a cos x – sin x O 6 sin æ + 6 cos e O 6 tan x + 6 sec x O 6 tanx +6 csc x O 6 cot…

A: We need to simplify the following expression 6cos2x-1sinxcosx-sinx

Q: 1. tan x csc x-secx cot x sin x-cos x sin x cos x

A: This is a problem related to trigonometric formula. General formula which use for solving 1 problem…

Q: Prove the identities Then use them to show that a. sinh 2x = 2 sinh x cosh x. b. cosh 2x = cosh²x +…

A: Here we have to use the given identities to prove.

Q: Prove: 1 + 1 = 2 sec? x 1-sin x 1+sin x

A: Prove   1/(1-sinx) + 1/(1+sinx) = 2sec2x

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

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: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos…

A: