Hi there!
We can begin by solving the left side:
tan²Θ - sin²Θ =
Rewrite tan:
[tex]\frac{sin^2\theta}{cos^2\theta} - sin^2\theta =[/tex]
Multiply sin²Θ by cos²Θ to get a common denominator:
[tex]\frac{sin^2\theta}{cos^2\theta} - \frac{sin^2\theta * cos^2\theta}{cos^2\theta}=[/tex]
Subtract:
[tex]\frac{sin^2\theta- sin^2\theta * cos^2\theta}{cos^2\theta} =[/tex]
Factor out sin²Ф from the numerator:
[tex]\frac{sin^2\theta(1 - cos^2\theta)}{cos^2\theta} =[/tex]
Rewrite 1 - cos²Ф as sin²Ф (Pythagorean identity)
[tex]\frac{sin^2\theta(sin^2\theta)}{cos^2\theta} =[/tex]
Simplify:
[tex]\frac{sin^4\theta}{cos^2\theta} =[/tex]
Split into sin and tan:
[tex]sin^2\theta * \frac{sin^2\theta}{cos^2\theta} =[/tex]
Rewrite:
[tex]sin^2\theta * tan^2\theta[/tex]
