Use fundamental Identities to find the exact value of the expression. Do not use a calculator.
Sin² 65° + cos² 65°=??..
How would I attempt to solve this problem??
1
(by definition)
find sin65 and square it. find cos 65 and suare it. then add the two answers together
To solve this problem using fundamental trigonometric identities, we can make use of the Pythagorean identity, which states that sin²θ + cos²θ = 1 for any angle θ.
In this case, we need to find the value of sin²65° + cos²65°.
Step 1: Apply the Pythagorean identity
sin²θ + cos²θ = 1
Step 2: Substitute the angle value
sin²65° + cos²65° = 1
Therefore, the exact value of sin²65° + cos²65° is 1.
Note: The Pythagorean identity is a key trigonometric identity that relates the sine and cosine functions. Memorizing this identity can be very helpful when solving problems involving trigonometric expressions.