Provide an appropriate response. Use the fundamental identity cosh² 1 - tanh2 x = = sech² x - sinh² x = 1 to verify the identity.

Q: Verify the following identity by algebraically turning one side into the other:…

A: we have to prove that1+tan2u1-sin2u=1

Q: please show all steps to verify a identity  (1/1+sinx)    -    (1/1-sinx)  =-2sinxsec2x

A:

Q: Differentiate the given sin (x² +1) 2 X

A: Sin(x2+1) To differentiate the given function

Q: Calculate the following. a. sin cos" (-) c. tan-(1)

A: To calculate the following trigonometric values of the functions.

Q: sec(-x) sin?x sinx X %3D

A:

Q: Evaluate * sin-lr xp= V1- x

A:

Q: The term 0.5(1-cos2x) is equal to

A: Given,          The term is 0.51-cos2x .

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

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

Q: Prove: Sin(x-pi/2) = -cosx

A:

Q: If sinX = -1/3 and cosX is positive, determine the exact value of cotX.

A: We know, cosx= ±√(1-sin2x) cotx= cosx/sinx

Q: sin (30)cos (32) %3D

A: Topic = Trigonometry    using formulascos 2x = 1-2 sin2xcos 2x = 2 cos2x - 1

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

A:

Q: sec² () = 1+ cos x 2.

A:

Q: Verify: 1. (sinx – cosx)² – 1 = -sin2x %3D

A: We can verify the statement as below