Solving a trigonometric equation with applying pythagorean identity

The video tutorial explains how to solve the trigonometric equation sine squared of Theta minus cosine squared of Theta equals zero. It demonstrates the use of trigonometric identities for substitution and simplification, and how to find solutions using the unit circle. The tutorial also covers finding all possible solutions by considering the periodic nature of trigonometric functions.

What is the initial equation that needs to be solved in the video?

• sine squared of Theta minus cosine squared of Theta equals zero

• sine squared of Theta plus cosine squared of Theta equals zero

• sine squared of Theta times cosine squared of Theta equals zero

• sine squared of Theta divided by cosine squared of Theta equals zero

Which identity is used to substitute for sine squared of Theta?

• sine squared of Theta equals cosine squared of Theta

• sine squared of Theta equals 1 plus cosine squared of Theta

• sine squared of Theta equals 2 minus cosine squared of Theta

• sine squared of Theta equals 1 minus cosine squared of Theta

What is the value of cosine squared of Theta after simplification?

• 1/4

• 3/4

• 1

• 1/2

On the unit circle, what is the angle where cosine of Theta equals sqrt 2 / 2 in the first quadrant?

• π / 2

• π / 4

• π / 3

• π / 6

How many solutions are there between 0 and 2π for the equation?

• 3

• 5

• 2

• 4

What is the method to find all solutions beyond 0 and 2π?

• Add π repeatedly

• Add π / 4 repeatedly

• Add 2π repeatedly

• Add π / 2 repeatedly

What is the general form for all solutions of the equation?

• π / 4 + π / 2R

• π / 4 + π / 4R

• π / 4 + πR

• π / 4 + 2πR