Trigonometric Formula's:
[tex]\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}[/tex]
[tex]\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }[/tex]
Given to verify the following:
[tex]\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a[/tex]
[tex]\texttt{\underline{rewrite the equation}:}[/tex]
[tex]\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )[/tex]
[tex]\texttt{\underline{apply distributive method}:}[/tex]
[tex]\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)[/tex]
[tex]\texttt{\underline{simplify the following}:}[/tex]
[tex]\rightarrow \sf 2cos^2 a + sin^2 a[/tex]
[tex]\texttt{\underline{rewrite the equation}:}[/tex]
[tex]\rightarrow \sf 2(1 - sin^2a ) + sin^2 a[/tex]
[tex]\texttt{\underline{distribute inside the parenthesis}:}[/tex]
[tex]\rightarrow \sf 2 - 2sin^2a + sin^2 a[/tex]
[tex]\texttt{\underline{simplify the following}} :[/tex]
[tex]\rightarrow \sf 2 - sin^2a[/tex]
Hence, verified the trigonometric identity.
