Example: Find ſ tan x dx

Q: → 61. y = In (tan¬ x)

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Evaluate cos° Зх dx

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Q: 4) | tan (x). sec(x) dx

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Q: If arc tan x + arc tan 1/3 = T/4, find the value of x. 1/2 1/3 1/4 1/5

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Q: 5

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Q: TU (sin³ x)√1 + cos x dx EN

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Q: tan x+ cot x) dx

A: Recall trigonometric identities, Substituting the values in above equation, we get

Q: Evaluate COs dx

A:

Q: Evaluate cos tan Vx² + 1

A: We have to evaluate the given trigonometric function.

Q: Division rule

A:

Q: Example 32. Evaluate sin x X dx

A: Sol:- ∫0∞ sinxxdxCompute the indefinite integral:Use the nonelementary integral:  ∫sinxxdx=SixAdd a…

Q: verify the identity tan(x/2) + cot(x/2) = 2 csc x

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Q: a. as x→. tanx- b. as x→ tan x→ E. as x→0", cotx→ d. as x→0*, cotx→

A: Given query is to find indicated limits.

Q: tan(x+D Dlim

A: We have to find the value of limx→-1tanx+1x+1. If we substitute x=-1 in the function, then we get 00…

Q: /tan x sin x cos x

A: given = ∫tan (x)sin (x) .cos(x)dx

Q: If tant =2, what is tan (t – #)?

A: Given

Q: Verify the identity: tan x + 1/tan x = 1/(sin x cos x)

A: To verify: tan x+1tan x=1sinx. cosx

Q: Find the value of § cot³(x) cosec“ (x).

A:

Q: Verify the identity tan (x+pi/4) = tan x+1/1-tan x

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Q: Verify the identity:cot x + tan x = csc x sec x.

A: The given identity is cotx+tanx=cscxsecx

Q: Establish the identity tan (x - 0) = - tan 0.

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Q: Evaluate ! d(cos x – x)

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Q: 2. a. arctan(-1) b. tanV3 C. tan-

A: a)tan-1(-1)=-π4b)tan-1(3)=π3

Q: tan(x)csc(x) cos(x)

A: Given,            Tan(x).cosec(x).cos(x)

Q: tan x+ cot x csc(2x) = %3D

A:

Q: Verify the identity: tan x + tan y = sin(x + y)/(cos x cos y)

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Q: Find if sin x +1= cos y

A: Given,           sinx+1=cosy

Q: If (tan r + sec x)² A + sin x В - sin x then A B =

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Q: Example 32. Evaluate 8 sin x X dx Gasts

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Q: practice question, I attached a photo

A: In order to compute the tan theta value, use the fact sin2 x + cos2 x = 1 .

Q: Write the expression as an algebraic expression in x for x > 0.tan (arccos x)

A: Recall the trigonometric identities, sin x=1-cos2x tanx=sinxcosx

Q: Find tan e if sin e = 1/3 and e terminates in QI. tan e =

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Q: Evaluate. S tan ()dx

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Q: 9. S tan x dx =

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Q: If sec A + tan A = x then sec A is?

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Q: Evaluate y' of y = tan-'(cosx).

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Q: show that if y=x/tan(x) then y'=cot(x)-csc(x)

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Q: dx Example: Evaluate 3 + sin x + cos x

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Q: y? sin (tan Sx|

A: We have to find derivative

Q: If tan(x+y) tan(x-y) = 1 then find the value of tanx

A: From the given data:

Q: If sec A+tan A= y then tan A =

A: Given,           secA+tan A=y

Q: tan 2x = Given that tan x = A

A: Solution-

Q: tan X If y = (Sin x)

A: y=sinxtanx Applying natural logarithm on both sides, we get ⇒lny=lnsinxtanx⇒lny=tanx lnsinx

Q: 3. If tan (x+ y) = and tan y what is tan x? %3D

A: Topic:- trigonometry

Q: If tan" x, show that ýe-2sincesy ye-25incesy

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Q: tan '6 (secx)"dx tan

A:

Q: Verify the identity: cot x + tan x = csc x sec x.

A: cot x + tan x = csc x sec x. L.H.S  = cot x + tan x           =  cosxsinx + sinxcosx           =…