Question

Cos4x=1-8sin²xcos²x prove that

Answer 1

Hey !!!

we know that

cos2¢ = cos²¢ - sin²¢

similarly ,

cos4¢ = cos 2× 2¢ = cos²2¢ - sin²2¢

=> cos²2¢ - ( 2sin¢ × cos¢ )²

•°• we know that sin2¢ = 2sin¢ × cos¢

=> cos²2¢ - 4 sin²¢ cos²¢

=> ( cos²¢ - sin²¢ )² - 4sin²¢ cos²¢

•°• we also know that .

cos2¢ = cos²¢ - sin²¢

=> cos⁴¢ + sin⁴¢ - 2sin²¢ cos²¢ - 4sin²¢ cos²¢

=> ( cos²¢)² + ( sin²¢ )² -6sin²¢ cos²¢

•°• a² - b² = ( a + b )² - 2ab

similarly using like this .

=> ( sin²¢ + cos²¢ )² - 2sin²¢ cos²¢ - 6sin²¢ cos²¢

=> 1 - 8sin²¢ cos²¢ prooved ♻ .

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Hope it helps you !!!

@Rajukumar111