Question

True or False. Explain your answer. csc^-1[csc(-pi/4)]=-pi/4 sec[sec^-1(sqrt3)]=sqrt3

Answer 1

Property of inverse functions:
$f(f^{-1}(x)) = x \\ \\ f^{-1}(f(x)) = x$

Therefore the answer to both is True.

Answer 2

Answer:

True

Step-by-step explanation:

Given : Expression $\csc^{-1}[\csc(-\frac{\pi}{4})]=-\frac{\pi}{4}$ and $\sec[{\sec^-1}(\sqrt3)]=\sqrt3$

To find: The given expression are true or false?

Solution :

In the given expression,

Applying Inverse trigonometric functions,

i.e, $f(f^{-1}x)=x$

or $\csc^{-1} (\csc x)=x\\\csc(\csc^{-1} x)=x$

and this true for all trigonometric functions.

So, if apply in the given expression the resultant we get is true.

$\csc^{-1}[\csc(-\frac{\pi}{4})]=-\frac{\pi}{4}$ is true

and $\sec[{\sec^-1}(\sqrt3)]=\sqrt3$ is true

Therefore, The given expressions are true.