do 6) I cos° 0 7 [(1- sin° 31)- cos3t dt 8) | tan (5x)· sec (5x) dx

Q: Q4// Find the value of csc(sec-1 2) + cos(tan=²(-V3)).

A: Here  given as Use some trigonometric formula as

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: S sin5 3 x cos' 3 xdx

A:

Q: Find   cos(u2)cos(u2)   if   secu=9.545

A:

Q: S(sinx – cosx)²dx COoSx

A: Given, ∫sinx-cosx2dx  We have to find the integral.

Q: y = e2* sin 2x + e3* cos 2x

A:

Q: Find sin y if sec y= (√30)/5 and tan y

A: Given,secy=305siny = ?tany = ?

Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

Q: ] 1 1-x² dx = tan¹(x)

A:

Q: cos X y = sin x +cosX

A:

Q: 4. tan²B + 1 = sec² B

A:

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: sec² (x) tan° (x)dx

A:

Q: 2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f)…

A: (a) Consider the given expression: sin-1-1 Sine gives negative one as it value at -π2. Therefore,…

Q: 4. cos' (sin (7 /6 )) 5. sin 1 (cos (π/ ) 6. tan (sin (3n/2))

A:

Q: quat sin-'(2x) + cos-'(3x) = 3

A:

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

A:

Q: Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(C

A: