Question

$\sqrt{1 - { \sin {}^{2} (115) }} \times \sec(115)$ the answer is 1 or -1​

Answer 1

Answer:

$\displaystyle{\sqrt{1 -{\sin {}^{2} (115) }}\times  \sec(115)=1}$

Step-by-step explanation:

Given  :

$\displaystyle{\sqrt{1 -{ \sin {}^{2} (115) }} \times  \sec(115)}$

We know :

$\displaystyle{\sin^2\theta+\cos^2\theta=1}\\\\\displayle{Rewrite \ as}\\\\\displaystyle{\cos\theta=\sqrt{1-\sin^2\theta}}$

Now :

$\displaystyle{\sqrt{\cos^2115} \times\sec(115)}\\\\\displaystyle{\cos115\times\sec(115)}$

We know reciprocal of cos

$\displaystyle{\cos\theta=\dfrac{1}{\sec\theta}}$

$\displaystyle{\dfrac{1}{\sec115}\times\sec(115)}\\\\\\\displaystyle{\implies1$

Thus the answer is 1 .