Use the fundamental identities to fully simplify sin(−x)cos(−x)sec(−x).

Q: Write the expression as an algebraic expression in x for x > 0.

A: Given, cos2tan-1x

Q: Verify that the equation is an identity. 2 sin x tan 2.r = 2 cos x - sec x

A:

Q: Find all values of x such that sin 2x = sin x and 0 <x< 2m.

A: sin 2x=sinx⇒sin 2x-sin x=0⇒2 sin x cos x -sin x=0⇒sin x2 cos x-1=0⇒sin x=0  or  2 cos x-1=0 sin…

Q: Simplify the following functions sin(tan^-1(x/2))= sin(2tan^-1(x/2))=

A: We have to simplify the following functions

Q: Show that the following is true. cos(X-pi/2) = sinX

A:

Q: Prove the identity. +x + sin 6. sin = cos x

A: Given, We have to prove the identity sinπ6+x+sinπ6-x=cosx

Q: Write the expression as an algebraic expression in x for x &gt; 0.

A: Since, we know that cos2 (x)=cos (2x)+12⇒2 cos2 (α)=cos (2α)+1By assuming α=12(cos-1x)⇒cos 12cos-1…

Q: Rewrite sin (x + in terms of sin x and cos x. Enclose arguments of functions in parentheses. For…

A:

Q: Rewrite cos ( x in terms of sin(x) and cos(x) 3 -

A:

Q: Graph the function ƒ(x) = sin 2x + cos 3x.

A:

Q: Rewrite cos(x−π6)cos(x-π6) in terms of sin(x)sin(x) and cos(x)cos(x)

A: This is trignometry problem

Q: Verify the identity : cos (x - π/4) = √2(cos x + sin x)/2.

A: We use cos(A-B)=cosAcosB+sinAsinB formula

Q: Write the expression as an algebraic expressionin x for x>0.   b.  tan (2 cos-1(3/x))

A: Given expression can be represents as: tan2cos-13x  for x&gt;0. Let us suppose θ=cos-13x  then the…

Q: Evaluate ∫sin2 x cos4 x dx.

A:

Q: Verify the identity: cos(3x) cos(x)(1 – 4 sin? (x))

A: we have to verify the given identity. the solution is following

Q: Rewrite cos x + 3 in terms of sin(x) and cos(x). COS

A:

Q: An equivalent expression to sin(-x) is: Oa) - sin(-x) b) sin(x) Oc) - sin(x) d) cos(x)

A:

Q: Use an identity to solve the equation tan x - sec x = 1 on the interval [0, 2π).

A: The given equation is tanx-secx=1.

Q: Rewrite  − 6 sin ( x ) − 3 cos ( x ) as  A sin ( x + ϕ ) A= ϕ=

A: see below the answer and calculation

Q: 2T Rewrite cos x + 3 in terms of sin(x) and cos(x)

A:

Q: Verify the identity: sin (x + π/2) = cos x

A: We have to verify the identity sinx+π2=cosx We know that sina+b=sina cosb+cosa sinb Using the…

Q: Verify the identity. 2 sin(x) cos(x) = 1 (sin(x) + cos(x))2 - 1

A:

Q: Rewrite sin ( x in terms of sin(x) and cos(x). 4 |

A: sin ( a - b) = sin a cos b - cos a sin b

Q: Rewrite cos x in terms of sin(x) and cos(x) -

A: Trigonometry problem...

Q: Write the expression as an algebraic expression in x for x > 0. 3 tan 2 cos -1 3 tan 2 cos

A:

Q: Use an identity to solve the equation cos 2x = cos x on the interval [0, 2π).

A: Given:cos2x=cosx on the interval [0,2π)Formula:cos2x=cos2x-sin2xsin2x=1-cos2x

Q: Verify the identity. COs x + 1 sin x + sin x I + X 500 2 csc X

A:

Q: Use identities to find values of sin 2x and cos 2x with the following condition. tan x = 2 and cos x…

A:

Q: (-) in terms of sin(x) and cos(x) 4 Rewrite sin x

A: Use formula Sin(A-B)=SinA.CosB-CosA.SinB

Q: prove the identity  sin(x) + sin(3x) = 4 sin(x) cos2(x)

A:

Q: Rewrite sin ( x + in terms of sin(x) and cos(x) 4

A: We know  sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Q: Evaluate sin(x) · In ( cos(x)) dx using substitution.

A:

Q: Rewrite sin x + in terms of sin(x) and cos(x). 3

A: We will use the below trigonometric identities to solve this

Q: Find the identical expression for the following. ​sin x(sec x- cot x) A. sec x  B. cotx-sinx c.…

A: The given expression is sin xsec x-cot x.

Q: Rewrite sin (z + in terms of sin(x) and cos(x)

A: Recall:  sin(A+B)=sin A cos B+sin B cos A We have, A=x, B=π3

Q: Choose the equivalent sin'x O 1- cos-x

A: Given sin^2(x)

Q: Write the expression as an algebraic expression in x for x > 0. sec sin-1 x2 + 36

A:

Q: and

A:

Q: Rewrite cos ( x in terms of sin(æ) and cos(x). 4 -

A: we know that cos(a-b)=cosa cosb+sina sinb

Q: what is the derivate of sin(x)cos(x)?

A:

Q: Rewrite cos ( x –) in terms of sin(x) and cos(x) 3

A: we know that cos(x-y)=cos(x)cos(y)+sin(x)sin(y)

Q: 3 Use basic identities to simplify sin° x + cos“ x sin x.

A: sin3x+cos2xsinx This can be written in the form sinx3+cos2ssinx Now simplify this expression  So…

Q: Verify the identity: sin 2x = 2cot x sin2 x.

A: Given, sin 2x = 2cot x sin2 x. Now consider the right-hand side we get,  R.H.S=2cotx…

Q: Verify the identity. 1- sin x + COs X 1 + sin x + cos X COS X | sin x + 1

A:

Q: Rewrite cos(x−3π/4)in terms of sin(x) and cos(x).

A: According to trignometry identity Cos(a-b) = Cosa Cosb +Sina SinbCos(π-θ) = - CosθSin(π-θ) = Sin θ

Q: Rewrite cos ( x in terms of sin(x) and cos(x). 3

A: Topic - Trigonometric identities Cos (a-b) = cos a cos b + sin a sin b