Verified answer

Step-by-step explanation:

1. sinθ=

cscθ

1

=

csc

2

θ

1

=

1+cot

2

θ

1

=

1+

tan

2

θ

1

1

=

tan

2

θ

1+tan

2

θ

1

=

1+tan

2

θ

tanθ

2. cosθ=

secθ

1

=

sec

2

θ

1

=

1+tan

2

θ

1

3. cotθ=

tanθ

1

4. cscθ=

csc

2

θ

=

1+cot

2

θ

=

1+

tan

2

θ

1

=

tan

2

θ

tan

2

θ+1

=

tanθ

1+tan

2

θ

5. secθ=

sec

2

θ

=

1+tan

2

θ

Step-by-step explanation:

Trigonometric Ratios

Sin θ Opposite Side to θ/Hypotenuse

Tan θ Opposite Side/Adjacent Side & Sin θ/Cos θ

Cot θ Adjacent Side/Opposite Side & 1/tan θ

Sec θ Hypotenuse/Adjacent Side & 1/cos θ