Question

question 6
which of the following is equivalent to
$(sin\theta + \cos\theta)^2$?
\\(\circ\\) $1 + 2\sin\theta\cos\theta$
\\(\circ\\) $\sin^2\theta + \cos^2\theta$
\\(\circ\\) $1 + \sin^2\theta\cos^2\theta$
\\(\circ\\) $1$

Explanation:

Step1: Expand the squared binomial

Use the formula $(a+b)^2 = a^2 + 2ab + b^2$:
$$(\sin\theta + \cos\theta)^2 = \sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta$$

Step2: Apply Pythagorean identity

Use $\sin^2\theta + \cos^2\theta = 1$:
$$\sin^2\theta + \cos^2\theta + 2\sin\theta\cos\theta = 1 + 2\sin\theta\cos\theta$$

Answer:

$1 + 2\sin\theta\cos\theta$