(a) Verify that tanh P-tanh Q 1-tanh P tanh ọ tanh( P – Q)

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

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

Q: sin zsiny de + cos zcosydy = 0 is a variable separable differential equation.

A:

Q: tan-¹ (sin) 0 - 4 O Оп 0-1/2

A: we know  that  sin(π2)=1let  y=tan-1(sinπ2)

Q: D cosh x dy + Cy Stnhx +e) dx - o +ě) dx =

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

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

A:

Q: Q1- Prove that coth x = 2 csch 2x + tanh x %3D

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Q: | sec(/I) tan(/) dr

A: We need to solve integral.

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

A:

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

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Q: tan u-tan v Prove tan( u – v) = 1+ tan u tan v

A: tanu-v=sinu-vcosu-v=sinucosv-cosusinvcosucosv+sinusinv     ∵sinx-y=sinxcosy-cosxsiny &…

Q: Star tan 5t dtl

A:

Q: 3 tan (x) sec (x) dx T) sec (x)dr

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Q: tan-1 3

A: tan-133

Q: 3D5 in.

A: The area of the circle can be computed using the formula: Area=π r2 Where, 'π' is the constant value…

Q: Sa sec ede tan' 0+9 tan e

A:

Q: What is tan(B)? 33 12 tan (B) = 2

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Q: 2) sec tan 4

A: Solution: The objective is to find the required value

Q: The evaluation of fet tan(et) dt O sec2(t) + c O -tan2 (e-t) - 1+c C sec? (e t) + c c tan? (et) + c…

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Q: tan A - tan B = I+ tan A tan B tan(A-B).

A:

Q: Sin t/ 1+ cos t = 1-cos t/ sin t

A: The given equation to prove is: sint1+cost=1-costsint Use the trigonometric identity, 1-cos2t=sin2t

Q: 8(1 + tan?(a)) da

A: Take out 8 from the integral.

Q: əz az +Y ay ax then x- If Z = tan-1(2) O 1 O 2

A:

Q: 2) tan-l 1 Vz 4) sin-! 6) tan-1V3 8) tan-l 0 V3 10) sin-! V3 12) tan- 2. 2. 3.

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Q: Derive the "addition formula" for tanh(x + y) in terms of tanh x and tanh y

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Q: Tan(3(x+iy))

A: Given below the detailed solution

Q: Let a be a real valued constant. Evaluate e-az sec(e¯a«)dx . O - In|sec(e-a*)+ tan(e¬a")|+C…

A: Given: - Let α be a real-valued constant. Then the indefinite integral is, I=∫e-αxsece-αxdx To find:…

Q: Let f(r) (3sin a + 5 cos z)tan r)tan f (x)-

A: