Question

Consider the Pythagorean Identity cos 2 ( θ ) + sin 2 ( θ ) = 1 . Divide both sides of this identity by cos 2 ( θ ) and simplify the resulting equation. What is the result? cos 2 ( θ ) + sin 2 ( θ ) = 1 cot 2 ( θ ) + 1 = csc 2 ( θ ) cos ( θ ) ⋅ sec ( θ ) = 1 1 + tan 2 ( θ ) = sec 2 ( θ )

Answer 1

Answer:

1   +  tan 2θ  = sec 2θ

Step-by-step explanation:

cos 2θ  + sin 2θ   =  1

Dividing  by cos 2θ we get

( cos 2θ  + sin 2θ ) /  cos 2θ   =    1 / cos 2θ

1  +  sin 2θ / cos 2θ   =   sec 2θ

And   sin 2θ / cos 2θ   = tan 2θ

Then

1   +  tan 2θ  = sec 2θ