Question

under root sec square theta minus 1 by sec theta​

Answer 1

Answer:

The required answer is $sin \theta$.

Step-by-step explanation:

Sec theta: The ratio of the hypotenuse and adjacent side is known as the sec theta of an angle in a right-angled triangle.

Given: under root sec square theta minus 1 by sec theta​.

To find: Solve the expression.

Solution:

The expression under root sec square theta minus 1 by sec theta​ means

$\frac{\sqrt{sec^{2}\theta-1}}{sec\theta}$

Solve this expression.

$\sqrt{\sec ^{2} \theta-1}=\sqrt{\tan ^{2} \theta}$                $\left(\because 1+\tan ^{2} \theta=\sec ^{2} \theta\right)$

Substitution.

$&=\tan \theta=\frac{\sin \theta}{\cos \theta}$

Expand now.

$&=\sin \theta \times \frac{1}{\cos \theta}=\sin \theta \sec \theta$

The expression is

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

Hence, the answer is $sin \theta$.

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