Question

Verify the identity:
secθcosθ/cotθ=tanθ

Answer 1

see explanation

Explanation:

Using the trigonometric identities

sec x =
`(1)/(cosx)` , cot x =
`(cosx)/(sinx)` , tan x =
`(sinx)/(cosx)`

Consider the left side

secΘ cosΘ ÷ cotΘ ← change ÷ to × and invert cotΘ

=
`(1)/(cos0)` × cosΘ ×
`(sin0)/(cos0)` ← cancel cosΘ on numerator/ denominator

=
`(sin0)/(cos0)`

= tanΘ = right side ⇒ verified

Answer 2

(identity has been verified)

Explanation:

Verify the following identity:

sec(θ) cos(θ)/cot(θ) = tan(θ)

Multiply both sides by cot(θ):

cos(θ) sec(θ) = ^?cot(θ) tan(θ)

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

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

cos(θ) (1/cos(θ)) = 1:

1 = ^?(cos(θ)/sin(θ)) (sin(θ)/cos(θ))

(cos(θ)/sin(θ)) (sin(θ)/cos(θ)) = 1:

1 = ^?1

The left hand side and right hand side are identical:

Answer: (identity has been verified)