Answer:
The simplified form of the expression is
[tex]\cos^2\theta(1+\tan^2\theta)=1[/tex]
Step-by-step explanation:
Given : Expression [tex]\cos^2\theta(1+\tan^2\theta)[/tex]
To find : The simplification of the expression?
Solution :
Step 1 - Write the expression
[tex]cos^2\theta(1+\tan^2\theta)[/tex]
Step 2 - Using the trigonometric property,
[tex]\tan\theta = \frac{\sin \theta}{\cos\theta}[/tex]
Substitute in place of [tex]\tan\theta[/tex]
[tex]=cos^2\theta(1+(\frac{\sin \theta}{\cos\theta})^2)[/tex]
[tex]=cos^2\theta(1+(\frac{\sin^2 \theta}{\cos^2\theta}))[/tex]
Step 3 - Taking LCM,
[tex]=cos^2\theta(\frac{\cos^2\theta+\sin^2 \theta}{\cos^2\theta})[/tex]
[tex]=cos^2\theta(\frac{1}{\cos^2\theta})[/tex]
Step 4 - Cancel the term
[tex]=1[/tex]
Therefore, The simplified form of the expression is
[tex]\cos^2\theta(1+\tan^2\theta)=1[/tex]
