Answer:
Therefore we have another identity:
[tex]\frac{cos^{2}\theta +sin^{2}\theta}{cos^{2}\theta*cos^{2}\theta}=\frac{1}{cos^{2}\theta*cos^{2}\theta}[/tex]
[tex]\frac{1}{cos^{2}\theta*cos^{2}\theta}=\frac{1}{cos^{2}\theta*cos^{2}\theta}[/tex]
Step-by-step explanation:
1) Considering the Pythagorean, or the Fundamental Trigonometric Identity Identity:
[tex]cos^{2}\theta +sin^{2}\theta =1[/tex]
2)Let's divide both sides, the left and the right one by:
[tex]cos^{2}\theta*cos^{2}\theta[/tex]
3) Since [tex]cos^{2}\theta +sin^{2}\theta[/tex] is equal to 1, then we can replace it. So
[tex]cos^{2}\theta +sin^{2}\theta =1\Rightarrow \frac{cos^{2}\theta +sin^{2}\theta}{cos^{2}\theta*cos^{2}\theta}=\frac{1}{cos^{2}\theta*cos^{2}\theta}\Rightarrow \frac{1}{cos^{2}\theta*cos^{2}\theta}=\frac{1}{cos^{2}\theta*cos^{2}\theta}[/tex]
Therefore we have another identity:
[tex]\frac{cos^{2}\theta +sin^{2}\theta}{cos^{2}\theta*cos^{2}\theta}=\frac{1}{cos^{2}\theta*cos^{2}\theta}[/tex]
