1- cot 0 17 1+cot 0 = sin' 0- cos² 0 %3D

Q: a. Express x = --3-8ż in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: a) x=-3-8ib) 2+5i2+2i

Q: |1-cos(0) If tan 0 > 0 and cos 0 < 0, sin = - 2

A:

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: 12 Find sin 2x, cos 2x, and tan 2.x if sin x= and x terminates in quadrant IV. 13 sin 2x %3D ? cos…

A:

Q: 7T then 3 If 0 = sin(0) equals Preview cos(8) equals Preview tan(0) equals Preview sec(0) equals…

A:

Q: (a) Prove that 1- cos 2.x NT = tan x, sin 2.x (b) Hence solve, for 0 < 0 < 2n, 1- cos 20 3sec? 0 – 7…

A: Solution(a): Prove that 1-cos2xsin2x=tanx LHS:1-cos2xsin2x=1-1-2sin2x2sinxcosx…

Q: Given the following informationabout one trigonometric function, evaluate the other five functions.

A: Solution: Consider the given trigonometric function is sin θ = -45    and π &lt; θ &lt; 3π2 sin θ =…

Q: 57T then 4° If 0 %3D - sin(0) equals cos(8) equals tan(0) equals sec(0) equals

A: Using trigonometrical identities.

Q: – 4T then 3 If 0 sin(0) = %3D cos(0) = Give exact values. No decimals allowed!

A:

Q: Verify the identity. sin 0-1 tan 0- sec 0 %3D cos e

A: Here we use basic identities of trigonometric ratios.

Q: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

A:

Q: Find the approximate value of cos (sin(-0.44). cos (sin -1(-0.44) = [ (Round to four decimal…

A: We will find the approximate value of cossin-1-0.44 in the following step.

Q: Show that sin ( 40) (cos 0) (4 sin 0 – 8 sin³ 0). %3D

A: To show: That sin 4θ=cos θ4 sin θ-8sin3θ. Formula used: sin A+B=sin A·cos B+sin B·cos A cos…

Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

A:

Q: If sin(0) >0 and cos(0) = - find tan(0). CO %3D tan(0) =

A:

Q: Which is an appropriate first step in verifying this trig equatio Cos 0 1-sin 0 sece + tan 0 It is…

A:

Q: 15 Find sin 2x, cos 2x, and tan 2x if tan x= and x terminates in quadrant III. 8 sin 2x = S ? cos 2x…

A:

Q: 4 TC 4) Find cos- given tan 0 2. where 0 <0 <- %3D 3.

A:

Q: A = -, find sin 2. If 90° <0 < 180° and cos 0 :

A:

Q: 4 5 Points ntegral of sin-cos-sin0 de has the form (e) +C. What should be the value of e =0?

A:

Q: Express the number 8√3-6i in the form R(cos(0) + i sin(0)) = Re, where R> 0 and - ≤ ≤T. NOTE: Round…

A:

Q: 1- cos 2x 1 a) sin 2x cot x

A:

Q: 6) If sin 0 = 0.2774, find cos 0. Round to four decimal places.

A: Given: sinθ=0.2774

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

A:

Q: 15 Find sin 2x, cos 2x, and tan 2x if sin x= and x terminates in quadrant I. 17 sin 2x cos 2x = tan…

A:

Q: 4. (cos? 6x + sin 6x – sin³ 6x)Zdx (Hint:factor out sin 6x first) 3 -

A: We need to evaluate ∫cos26x+sin6x-sin36x12dx Using the identity  cos2y+sin2y=1⇒cos2y=1-sin2y…

Q: 8. Prove that tan? 0 + cos? 0 + sin² 0 = sec² 0. %3D

A: Explanation and solutions is given below....

Q: Suppose that sin 0 = V10 and 90° < 0 < 180°. Find the exact values of sin and tan- JT sin 2 %3D…

A:

Q: 7. Prove: cos(0 + 2) 7) = sine.

A:

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: 1+cos 4x Express without double angles. sin 4x O (cot a + tan x) O ÷(cos x 글 (cos sin x) - O (cot a…

A:

Q: 7. Consider the identity _2 tanr 1+tan z sin(2r). (a) Verify the identity. (b) Find sin (4) if tan…

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: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function

Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: VERIFY THE IDENTITIES

A: To verify

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 5 sin 0 – 4 cos 0 e of 5 sin 0 + 4 cos 0 is

A:

Q: Q3-Prove that (cos30=cos³ 0-3cos 0 sin? 0)

A: Using compound angle formula &amp; trigonometric identities.

Q: 1. If 0° <0< 90° and sin 0 = , find sin 20. %3D

A:

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: TT CoS-+COs sin 3 = sin Prove that Sin 3 - 6. 6. 2.

A:

Q: 1- cos 0 1+ cos 0 sin 0

A:

Q: Recall that sin² 0 means (sin 0)². V5 find sin2 0. If sin 0 = 3 %3D sin? 0 = %3D

A:

Q: 50 a) Sin 25 b) Sin- Sinl0 =? Cosl0° Sin 5° = x, Cos 5° =y Sin 105° - ?

A:

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.