1. Prove: \(cos^2 x/cotx = sinxcosx\)

2. Prove: (secx cscx) / cotx = sec^2 x

3. Prove: (secx cscx )/ csc^2 x = tanx

4. Prove: (tan^2 x cosx)/ 2secx = 1/2 sin^2 x

5. Prove: \(Tanx/secx = sinx\)

Mathrules Oct 28, 2019

#1**0 **

2 -

Verify the following identity:

(sec(x) csc(x))/cot(x) = sec(x)^2

Multiply both sides by cot(x):

csc(x) sec(x) = ^?cot(x) sec(x)^2

Write cotangent as cosine/sine, cosecant as 1/sine and secant as 1/cosine:

1/cos(x) 1/sin(x) = ^?cos(x)/sin(x) (1/cos(x))^2

(cos(x)/sin(x)) (1/cos(x))^2 = 1/(cos(x) sin(x)):

1/(cos(x) sin(x)) = ^?1/(cos(x) sin(x))

The left hand side and right hand side are identical:

**(identity has been verified)**

Guest Oct 28, 2019

#2**0 **

3 -

Verify the following identity:

(sec(x) csc(x))/csc(x)^2 = tan(x)

Multiply both sides by csc(x):

sec(x) = ^?csc(x) tan(x)

Write cosecant as 1/sine, secant as 1/cosine and tangent as sine/cosine:

1/cos(x) = ^?1/sin(x) sin(x)/cos(x)

(1/sin(x)) (sin(x)/cos(x)) = 1/cos(x):

1/cos(x) = ^?1/cos(x)

The left hand side and right hand side are identical:

**(identity has been verified)**

Guest Oct 28, 2019