Question

If cos(θ)=sin(θ), find cos(θ), tan(θ).

a) cos(θ)=1,tan(θ)=1
b) cos(θ)=√ 2/2,tan(θ)=1
c) cos(θ)= √2 /2,tan(θ)= √2 /2
d) cos(θ)=1,tan(θ)= √2/2

Answer 1

To find the values of cos(θ) and tan(θ) when cos(θ) = sin(θ), use trigonometric identities. Solve for θ using the Pythagorean identity and find that cos(θ) = √2/2 and tan(θ) = √2/2.

Step-by-step explanation:

To find the values of cos(θ) and tan(θ) when cos(θ) = sin(θ), we can use trigonometric identities and solve for θ. First, let's rewrite the equation cos(θ) = sin(θ) as sin(θ) - cos(θ) = 0. Then, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to rewrite the equation as 2sin²(θ) - 1 = 0. Solving this quadratic equation, we find sin²(θ) = 1/2, which means sin(θ) = ±√2/2. Since cos(θ) = sin(θ), we have cos(θ) = ±√2/2. Therefore, the correct answer is option C: cos(θ) = √2/2 and tan(θ) = √2/2.