In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. W...

Question

In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c. tan(-t) - tan t

Accepted Answer

Hello everybody I have today today we're going to be looking at this question that states rewrite the following expression in terms of m if tangent of open parentheses, a closed parentheses equals M. Now the expression given is negative tangent of open parentheses, negative a closed parentheses plus tangents of open parentheses. A close parentheses. Now the answers given are a negative two M B two MC zero N D M. Now, before we can get into actually rewriting, let's recall a rule about tangent. So we can recall that tangent of open parentheses, negative acts closed parentheses is equal to negative tangent of open parentheses, positive acts closed parentheses. So these two things are equal to each other. And we can use that to our advantage to rewrite our expression. So let's rewrite. Let's write the expression once again. So we had negative tangent of open parentheses, negative A plus tangents of open parentheses. A closed parentheses. Now this can be rewritten as using the recall rule we have that this will be negative open bracket, negative tangent of a closed bracket plus tangent A. So all we did there was use our recall rule. We had tangents of negative A and that will be turned into negative tangents of A. But we have to include the negative that was already in front of our expression. So we take it out of the brackets. So now we have a negative multiplied by a negative, which is a positive. So we'll have tangent of A plus tangent of A and we know that tender of A is M. So we have M plus M which is equal to two M or in this case, answer choice B. So all we had to do here was recall a simple tangent rule and we can go ahead and rearrange our expression. So I hope that was helpful. And until next time.

In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c. tan(-t) - tan t

Key Concepts

Trigonometric Identities for Negative Angles

Definition of Tangent in Terms of Sine and Cosine

Algebraic Manipulation of Trigonometric Expressions

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