96. Using trig identities (NO CALCULATORS ALLOWED!!), prove the peculiar formula of John Machin (1706): TT -1 = 4 tan-1 4 tan 239 1 and then attack B= tan(4a - B) with 239 -1 and B tan (HINT: Introduce a = tan' = your trig identities.)

Q: 1 in tan 3 +coS -1

A:

Q: 4. If cos(x) = -, and x lies in the 3rd quadrant, find tan(). -2 2.

A: Given query is to find the value of indicated function.

Q: 13. If tan(x) = 3/2 and cos x <0, find the exact value of sec x. %3D

A: Given, tanx = 3/2  cos x &lt; 0   We have to find sec x

Q: 4 Suppose that sine = and <0<. Find the exact values of cos and tan Cos Undefined tan Continue O

A:

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

A: Using trigonometrical identities.

Q: 15 and x terminate: 8. Find sin 2x, cos 2x, and tan 2x if tanx = sin 2x |3| cos 2x

A:

Q: B) Prove that: 1-tan? 0 cos? 0 – sin? 0 - 1+tan? 0

A: Such identities can be proved by taking one side of the identity and proving it as equivalent to the…

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: Approximate all solutions to tan(4 ·x)² – 2 ·tan(4 ·x)– 15=0 in the interval [0°,360°) x =

A: Given equation (tan 4x)2-2 tan 4x-15=0

Q: Suppose that tan 0 = - and 90° <0 < 180°. 4 Find the exact values of cos and tan 2 믐 JT - 0 cos %3D…

A: giventanx=-34   90°&lt;x&lt;180°  we know that…

Q: 13. Find the value of tan 0/2, if sin e=-4/5 and 0 in QIII. 1/2 2+V3 -2

A:

Q: 4. Find the exact value of tan 45°. Enter your next step here

A: The exact value of tan 45∘can be calculated on the basis of geometric property i.e., The direct…

Q: Find sin 2x, cos 2x, and tan 2x from the given information. 4 cos x = csc x < 0 5 sin 2x = cos 2x =…

A: Given that , Cos(x) = 4/5.  We know that , Sin2(x) + Cos2(x) = 1 Implies , Sin2(x) = 1 - Cos2(x) Or…

Q: ) 3cos2(x) − 4cos(x) + 1 = 0 over [0,2π) 4) Solve tan 2x = −1 over [0,2π)   Note: Please answer…

A:

Q: 2. Express sin40 and cos40 in terms of powers of sin 0 and cos e only, respectively.

A:

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: Can you please help me with my verify the identity problem? 1 + sec^2x / 1+ tan^2x = 1 + cos^2 x

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx=- 1 and x terminates in quadrant II. sin 2x %3D cos 2x %3D…

A:

Q: 2 _ 2 if tane + sin0= m and tan0 – sin0 = n ,show that m² – n´ = 4 mn

A:

Q: Find sin(2x), cos(2x),and tan(2x) from given information. sex(x)=6 , x in Quadrant IV • sin(2x) =…

A:

Q: Find tan 0 if sin 0= 1/4 and 0 terminates in Q1

A: Given, θ terminates in Q1 So, tan θ i s positive

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

A:

Q: Solve 4 tan x * cos^2 x = 1 for 0 ^ 0

A:

Q: 57 tan 4 177 Determine the value of x if D, sin(7-x)= csc 3 6. where 0sxST.

A:

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: Find an algebraic formula for cos (tan-1 u + sin¬1 v), then use that formula to 1 compute cos…

A: given function ,  costan-1 u + sin-1 v  ..........................eq.(1) now we have to find an…

Q: 5л Compute the exact value of tan ( + 4 ). 6.

A:

Q: 4. Without using your calculator – show your work Evaluate tan ( – 0),when tan (0) = 1/3

A: Solution: The objective is to evaluate the given equation

Q: 2) Suppose tan 0 =7 and sin 0 <0. Compute sin 0 and cos 0. Exact answers are required.

A: Consider the given equation, tanθ=7 Since, there is sine negative and the value of tangent is…

Q: 7.6, #1 Find the exact value of the expression whenever it is defined. sin- (-) = b. tan-(-V3) =

A:

Q: 4. Use an identity to find the value of tan (6– 180°). O - tan 0 tan 0 1 O-1

A: 4. We need to evaluate the value of the following quantity tanθ-180° Identity Used : tanA-B =…

Q: tan 30 + 2S in Go +Cos 30 -tan 60 4.

A:

Q: how many solutions does (tan(x)-4)(cot(x)-2)(5cos(x)-6)(cos(x))=0 have in the interval [0,2pi]

A: Given:

Q: 12 Suppose that tan 0 =-· and 90°<0<180°. 5 Find the exact values of cos and tan 믐 cos Undefine 2…

A:

Q: Find the exact value of sin 20 if tan 0 with 0 in QII. 4 %3D O - 8 17 13 17 8 17 17 o 4V17 17

A:

Q: tan? 20° – sin? 20° Compute: Show your work. tan² 20° sin² 20°

A: Given  tan220°-sin220°tan220°sin220°

Q: then tan 0 is equal to If tan 4. %3D 3

A:

Q: 4. Find the exact value of sin if cose 2 3 and e is in QIII. cose =-- |

A: According to question,Given conditions,cos θ = -35,θ is in third quadrant.

Q: 4 If cos x = csc x < 0, then sin 2x = cos 2x = tan 2x = ||

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx 2 and x terminates in quadrant I. sin 2x cos 2.x !! tan 2.x

A: Given, tan x = 2 x terminates in quadrant in I We have to find the value of sin2x, cos2x and tan2x

Q: 12. sin 2t – tan t = tant cos 2t - HINT: You will use a reciprocal identity.

A: use the formula

Q: 2) Find the EXACT value of cos if tan(0) = 3 and sin(0) < 0

A:

Q: Suppose that π/2≤θ≤π, sin(θ)=2/10, find tan(θ)=______. (round to 3 decimal places)

A: Given:-sinθ=210π/2≤θ≤π

Q: 1. When does csc z = 2? 2. When does tanʼr = 1? 3. When does cotx = 0? 4. When does secx = -2?

A: Trigonometric equation

Q: 5) Find the exact value of cos [tan--si sin-" (-): 12

A:

Q: If tan θ= √2/5 and π (less than) θ (less than) 3 π/2, find the exact value of cos 2 θ

A: Given tanθ=25   If π&lt;θ&lt;3π2 then  cos2θ=?

Q: Find tan 3. (9, 12) ? tan 3 = Give your answer in lowest terms.

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx = and x terminates in quadrant I. 5 sin 2.x cos 2.x tan 2.x

A:

Q: Find tan o if sin 0=2/3 and 0 terminates in q1

A: