I would certainly like to recognize if there is a basic strategy to solve equation looking favor this:

\$\$ an(sec^-1 4)\$\$

without using a calculator (you need to find the specific value)?

How to proceed?

Imagine a right-angled triangle through one leg \$k\$ and hypotenusage \$4k\$ and also angle \$ heta\$ between them. Then \$cos heta = frack4k= frac14\$ and \$sec heta = 4\$, making \$sec^-14 = heta\$.

The oppowebsite leg is \$sqrt(4k)^2-k^2=sqrt15k\$ and so \$ an(sec^-14) = an heta = fracsqrt15kk=sqrt15\$. Now you may need a calculator.

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Let \$sec^-14= hetaimpliessec heta=4\$

Now, \$ an^2 heta=sec^2 heta-1\$

Finally utilizing the definition of the principal worth of \$sec^-1,00\$

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