Question

Express cos A and tan A in terms of sin A.

Hint:

Using identities is often faster and more general than building triangles for variable-based proofs.

Answer 1

Step 1: Use Fundamental Identity
We know:
sin²A + cos²A = 1

Rearrange:
cos²A = 1 − sin²A

Since A is acute,
cos A is positive.

So,
cos A = √(1 − sin²A)

Step 2: Express tan A in terms of sin A
We know:
tan A = sin A / cos A

Substitute cos A:
tan A = sin A / √(1 − sin²A)

Final Answer:
cos A = √(1 − sin²A)
tan A = sin A / √(1 − sin²A)