Question

Simplify quantity 1 minus sine squared theta divided by cosine squared theta. .

Answer 1

(1 - sin^2 ¤)/cos^2¤
=(1/cos^2 ¤) - (sin^2¤/cos^2¤)
=(sec^2¤) - (tan^2¤)
=1 [1+ tan^2¤=sec^2¤]

Answer 2

Answer:

$\frac{1-sin^2\theta}{cos^2\theta}=1$

Step-by-step explanation:

Given : Quantity 1 minus sine squared theta divided by cosine squared theta.

or $\frac{1-sin^2\theta}{cos^2\theta}$

To simplify: The given quantity

Solution :

Step 1- Write the given quantity

$\frac{1-sin^2\theta}{cos^2\theta}$

Step 2- Separate the denominator to both the numerators

$\frac{1}{cos^2\theta}-\frac{sin^2\theta}{cos^2\theta}$

Step 3- Simplify the form

$sec^2\theta-tan^2\theta$

Step 4- Applying the property of trigonometry $[1+tan^2\theta = sec^2\theta]$

$sec^2\theta-tan^2\theta=1$

Therefore, $\frac{1-sin^2\theta}{cos^2\theta}=1$