Answer:
See below
Step-by-step explanation:
A > [tex]Sin^{2} x + cos^{2} x = 1 \\[/tex]
Divide both side by sin^2 x , and we get
[tex]\frac{sin^2 x}{sin^2 x} + \frac{cos^2 x}{ sin^2 x} = \frac{1}{sin^2 x}[/tex]
[tex]1+ cot^2 x= cosec^2 x[/tex]
Subtracting cosec^2 x from both sides we get
[tex]Cosec^2 x - cot^2 x = 1[/tex]
B>lets break tan θ into its components tan θ = sin θ / cos θ and cot θ = 1/ tan θ
Tan θ + cot θ= Sin θ/cos θ + cos θ/ sin θ = sin^2 θ + cos^2 θ / sin θ cos θ= 1/ sin θ cos θ = sec θ cosec θ
