1. sec x – tan x sin x = secx 1+cosx 2. = cscx + cotx sinx secosine 3. tan0+cot0 sin20 secß 4. tanß = 1 cotß cosß

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: 3 Find sin 2x, cos 2x, and tan 2x If cosx= and x terminates in quadrant II. sin 2x cos 2x tan 2x

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Q: 6. cos x(csc x secx) secx) cotx

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Q: If y = sin x, then y' = - cot x sin x - tan x sec x sec x -sin x - Cs X tan x cos X CSC X

A: Given function is y=sinx. Differentiating the given function with respect to x, we get…

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…

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Q: lim, 0 tan² (7x) cot(11x) (r+7)sinx

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Q: 2 (tan²x + 1)√sin2x.dx= (tan², 0

A: Find your answer below

Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

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

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

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

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Q: Verify. a. (2 tan x ) / (1 + tan2 x) = sin(2x) b.  1 / (1 − sin θ) + 1 / (1 + sin θ) = 2 sec2 θ c. 1…

A: Part a)Given:

Q: 3. (6れ)-) ANCTAN X (x+1) ² -y=ARCTAN

A: To expand the given function :

Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: 2- tan²x + 1 + tanx secx = 1+sinx cos²x

A: To show that , tan2x+1+tanx.secx=1+sinxcos2x

Q: y (3, 4) sin(0) = %3D cos(0) = tan(0) = csc(0): sec(0) : cot(0) = %3!

A:

Q: Beginning with [sin(x)]^2+[cos(x)]^2=1, prove that 1+[cot(x)]^2=[csc(x)]^2

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Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 15) tan- -1 Vz 17) cos -1 19) tan 1

A: topic - Inverse trigonometric ratios

Q: Evaluate S tan'x sec'x dx sec x 2 secx sin x - 2 sin'x + sin'x +C 3 3 Option 1 O Option 2 - cos'x +…

A:

Q: +sin 0 1-sin 0 4 tan 0 sec 0 -sin 0 1+sin 0

A: Given query is to prove using identities of trigonometric functions.

Q: Find the exact value of sin(x - y) if sin x = 3 ≤ y ≤ 2. on ≤x≤ and sin y=-3 on

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Q: Determine the value of  tanz if sinz + cos z=0.2 and pi>z<pi/2

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Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

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Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

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Q: Subject find derivatines of the first derivatives in volving differe and questients? 4 %3D COSX tanx…

A: Derivatives of function

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

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Q: 2) Verify. cot8 ese 6 %3D sin 6 tan 6

A: Use the following identities:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information.   sin(x) =  5 13,   x in Quadrant I…

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: Find the equation of the tangent line to the astroid x = cos° (0), y = sin³ (0) at 0 = 5. (Express…

A: The given equation of the astroid:x=cos3θ and y=sin3θWe need to find the tangent line to the astroid…

Q: 1+ cos x sin x 7. Verify: ¹ 11 csc x + cotx

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Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: cos^2x+sin^2x/cos^2x=

A:

Q: verify tan(y)/csc(y)=1/cos(y)−1/sec(y)

A: Given data:     The given trigonometric expression is: tan(y)/csc(y) =1/cos(y) -1/sec(y).     To…

Q: 1. cos t (1 + tan²t) sin ß sec ß + cos ß csc ß 2.

A: Given : 1. cost1+tan2t2. sinβsecβ+cosβcscβ

Q: If cos(x)=sin(x)=0.5 , find the following:   1) (sec(x))^3 2) sin(2x)+(cos(x))^2 3)…

A:

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: (12) ſ sin²x cos²x dx sin4x sin4x 8. 4 16 Option 1 Option 2 sin2x - 8. Option 3

A:

Q: 1 (tan x + cot х) sec x %D 1/cosx 1/sinx 1

A: Given query is to find the correct option for the expression.

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: 1. cos () 2. tan (7) 3. sin () Moli 4. sec (-660°) gnideil 5. csc (– 13) .ww 14T 6. . cot ()

A: Given

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: 1) B = cos 30 + sin² 0 tan 2x 2) y = 1-cot 2x 3) w = 2 csc(1 – 3x)

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: Differentiate the following: 1. sinocose 2 csce -coto tan@sece 3 (cos 0-1)0

A: Topic:- derivatives  Note :- as per our guideline only first three subparts need to answered

Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…