Question

Which of the following is equivalent to the expression? 

	A.
	B.
	C.
	D.

 

Which of the following is equivalent to the expression? 

	A.
	B.
	C.
	D.

Which of the following is equivalent to the expression? 

	A.
	B.
	C.
	D.

 

Answer 1

1) The expression is sin(θ) csc(θ)

Recall the reciprocal identity of sin(θ) is csc(θ).

sin(θ)csc(θ) = sin(θ)[ 1/sin(θ)]

= 1

Option D is correct.

Answer 2

2) The expression is [sec(θ)]/[ csc(θ)]

= [1/cos(θ)]/[1/sin(θ)]

= [1/cos(θ)]sin(θ)

= sin(θ)/cos(θ)

= tan(θ)

Option C is correct.

Answer 3

3) The expression is [ sec² (θ) - 1]/sin²(θ)

From pythagorean identities 1+ tan²(θ) = sec² (θ)

= [ 1+ tan²(θ) - 1]/sin²(θ)

= tan²(θ) / sin²(θ)

= [sin²(θ)/cos²(θ)]/ sin²(θ)

= 1/cos²(θ)

= sec²(θ)

Option D is correct choice.