Simplify sin(pi/6)^2+cos(pi/6)^2

Problem

sin(π/6)+cos(π/6)

Solution

1. Identify the trigonometric identity applicable to the expression. The Pythagorean identity states that for any angle θ the sum of the squares of sine and cosine is equal to 1

sin(θ)+cos(θ)=1

2. Substitute the specific angle θ=π/6 into the identity.

sin(π/6)+cos(π/6)=1

3. Verify by evaluating the individual trigonometric functions. We know that sin(π/6)=1/2 and cos(π/6)=√(,3)/2

(1/2)2+(√(,3)/2)2

4. Simplify the squared values and sum them.

1/4+3/4=1

Final Answer

sin(π/6)+cos(π/6)=1

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