Q 9 Prove that sin r is continuous by proving that limn0 sin(a + h) = sin(a) Va ER. (HINT: use sin x addition of angles formula). %3D . Q 8 Find all points (if any) where the tangent to p(x) = x³ – 6x2 +9x – 50 is horizontal 3D%D -

Q: EX:what is L sin²t

A: First we have, sin2t=12×2sin2t       =121-cos2t Now L1=1s,Lcos2t=ss2+22=ss2+4 then we find Lsin2t

Q: Write the trigonometric identities if applicable. 1. For the function f(x)=tan x, show that…

A:

Q: 4 A. sec* t- sec² t = tan´ t+tan* t

A: The given identity is,sec4t-sec2t=tan2t+tan4t

Q: 8+tan x dx 1-sin?x i.

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Q: Find f'x) usig the denivative rules, f (x) = 2 Sinx - COSX + tan X

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Q: et - e- е limr0 2 sin x

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Q: VI. Find the exact value of the expresssion: a) cos(sin=1) b) tan(sin¬'#)

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Q: B) prove du d 1. sec u = secu tan u %3D dx dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: d tan x sec* x dx (Let u tan x.)

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Q: dx sin² x cos²x 10. The value of f; A sinx-cosx+C B. cos x– sin x+C C. tanx-cotx+C D. cotx-tan x + C

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Q: sin x tan : :: cot : Cos x

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Q: Evaluate p* sin 0 de dr.

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Q: Differentiate. sin(0) f(0) 1 + cos(0) f'(0) %3D II

A: Differentiate

Q: 2. S 2 tan x secx - tan x d.r

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Q: By using u = tan 0, evaluate tan 0 sec*e de.

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Q: x sin x cos x Evaluate : dx. sin x + cos'x

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Q: Show that tan-1 ( 1/v ) = π/2 - tan-1 v, if v > 0.

A: To prove tan-11v=π2-tan-1v, let  x=tan-1v then tan x=v1tan x=1v Since  tanx=1cotxcotx=1v ⋯ (1)

Q: 7. lim a sin(1/a) =

A: In this question we need to find the limit of given function

Q: Differentiate y = (sin x)e A. (sin x)e (cot x- 2ln sinx) B. (sin x)e (cot x – In sinx) C. (sin x)e…

A: To find the derivative.

Q: Let sinx =where sxs. Determine the value of: 5 (a) cos x (b) tan x

A: Trigonometric functions are real functions which relate an angle of a right angled triangle to…

Q: Which of the expressions below are equivalent? Which are not? Explain. i. sin '(x) ii. csc(x) iii.…

A: It is known that sin-1x can also be written as arcsinx.

Q: tan? x – cot2x = sec2 x – csc? x - tanx-sinx = 1- cosx tanx

A: To prove :- 5.tan2(x) - cot2(x) = sec2(x) -csc2(x)  6. (tan(x) -sin(x))/tan(x) =1-cos(x)

Q: Q1 If A= Cosa sina -Sina Cosya Cosa Sin ya Prare that A Sin ya Cosya

A: Given . We have to prove

Q: Prove cos* x – sin* x =1–2sin² x

A:

Q: Evaluate lim i+ cos rj sin (at)

A: Follow the procedure given below.