Determine whether each statement is true or false. If false, tell...

Question

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42.

1 tan² 60° = sec² 60°

Accepted Answer

Hey, everyone here, we are asked to check whether the following statement is true or false. Here we are given one plus tangent squared of 30 degrees is equal to second squared of 30 degrees. Here we have two answer choice options, answer choice, a true or answer B false. So in order to determine if our given statement is true, we need to confirm that the left hand side of our equation is equivalent to the right hand side of our equation. So that means we want to start by finding the values for the left side and the right side of the equation individually. So starting with the left side again, recalling we have one plus tangent squared of 30 degrees. We first want to recall that tangent of 30 degrees has an exact value of the square root of three divided by three. So now substituting this value into the left side of our statement, we have one plus the quantity of the square root of three divided by three squared. And now we just want to start simplifying. So we have one plus three divided by nine, simplifying by reducing the fraction, we have one plus one third. And now summing to the two values, we have four thirds which has a decimal approximation of 1.3 repeating. And so now we want to find the value of the right side of our equation where we need to recall that we have second squared of 30 degrees. So now we want to recall that the value of second of 30 degrees is two divided by the square root of three. And now substituting in this exact value for second into the expression, we have the quantity of two divided by the square root of three squared. And now simplifying we have four divided by three. And we know that the decimal approximation of four thirds is 1.3 repeating. And so now we see that we do in fact have the left-hand side of the equation equivalent to the right hand side of the equation. And therefore, we can conclude that our given statement is true. And so we are left with answer choice. A where again our statement is true. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. 1 tan² 60° = sec² 60°

Key Concepts

Tangent and Secant Functions

Pythagorean Identity

Calculator Use in Trigonometry

Watch next