Question:
What is the exact value of the expression sec60° + csc30° ?
Answer:
4
Solution:
sec60° + csc30° = ?
[tex]\large {\sf cos60^\circ = \frac{1}{2} }\\\\\sf but,\\\large {\sf sec60^\circ = \frac{1}{cos60^\circ} \;\;(reciprocal \;identity)}\\\\\sf hence,\\\large {\sf sec60^\circ = 2}\\\\\sf but,\\{\text {\sf $\sf csc30^\circ = sec60^\circ$ (co-function identity)}}\\\large {\sf csc30^\circ = 2}\\\\\sf therefore,\\\large {\sf sec60^\circ + csc30^\circ} = \\\large {\sf = 2 + 2}\\\large {\sf = 4}\\[/tex]
[tex]\therefore \;\large\boxed{\text{\sf The value of the expression is 4}}[/tex]
* as always, double check my answers for errors or carelessness.
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