sin ² ( π/4 - A) + sin² ( π/4 + A ) এর মান কোনটি?

Explanation:

Another Explanation (5): sin² ( π/4 - A) + sin² ( π/4 + A ) এর মান নির্ণয়: আমরা জানি, sin(a - b) = sin a cos b - cos a sin b এবং sin(a + b) = sin a cos b + cos a sin b সুতরাং, sin ( π/4 - A) = sin(π/4)cos(A) - cos(π/4)sin(A) = \(\frac{1}{\sqrt{2}}\)cos(A) - \(\frac{1}{\sqrt{2}}\)sin(A) এবং, sin ( π/4 + A) = sin(π/4)cos(A) + cos(π/4)sin(A) = \(\frac{1}{\sqrt{2}}\)cos(A) + \(\frac{1}{\sqrt{2}}\)sin(A) এখন, sin² ( π/4 - A) + sin² ( π/4 + A ) = [ \(\frac{1}{\sqrt{2}}\)cos(A) - \(\frac{1}{\sqrt{2}}\)sin(A) ]² + [ \(\frac{1}{\sqrt{2}}\)cos(A) + \(\frac{1}{\sqrt{2}}\)sin(A) ]² = \(\frac{1}{2}\)[cos²(A) - 2cos(A)sin(A) + sin²(A)] + \(\frac{1}{2}\)[cos²(A) + 2cos(A)sin(A) + sin²(A)] = \(\frac{1}{2}\)[cos²(A) + sin²(A) - 2cos(A)sin(A) + cos²(A) + sin²(A) + 2cos(A)sin(A)] = \(\frac{1}{2}\)[1 - 2cos(A)sin(A) + 1 + 2cos(A)sin(A)] [ যেহেতু cos²(A) + sin²(A) = 1] = \(\frac{1}{2}\)[2] = 1 অতএব, sin² ( π/4 - A) + sin² ( π/4 + A ) = 1 🥳🎉