Question

Verify the identity: secθcosθ/cotθ=tanθ

Answer 1

Answer:

(identity has been verified)

Step-by-step 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)

Answer 2

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sec x = $\frac{1}{cosx}$ , cot x = $\frac{cosx}{sinx}$ , tan x = $\frac{sinx}{cosx}$

Consider the left side

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

= $\frac{1}{cos0}$ × cosΘ × $\frac{sin0}{cos0}$ ← cancel cosΘ on numerator/ denominator

= $\frac{sin0}{cos0}$

= tanΘ = right side ⇒ verified