(sinθ+cosθ)²+(sinθ-cosθ)²=?

Explanation:

Another Explanation (5): \( \begin{aligned} &(\sin\theta + \cos\theta)^2 + (\sin\theta - \cos\theta)^2 \\ &= (\sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta) + (\sin^2\theta - 2\sin\theta\cos\theta + \cos^2\theta) \\ &= \sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta + \sin^2\theta - 2\sin\theta\cos\theta + \cos^2\theta \\ &= \sin^2\theta + \cos^2\theta + \sin^2\theta + \cos^2\theta \\ &= 1 + 1 \quad [\because \sin^2\theta + \cos^2\theta = 1] \\ &= 2 \end{aligned} \) সুতরাং, \( (\sin\theta + \cos\theta)^2 + (\sin\theta - \cos\theta)^2 = 2 \)। 🎉