Question

Evaluate 2sin (2x+y) cos (x-2y)?? Step by step please

Answer 1

★ TRIGONOMETRIC EQUATIONS ★

Universal identity →

☣ SIN (A) + SIN (B) = 2 SIN (A+B/2) COS (A-B)/2

☣ HERE, we found the same relationship between given equality ...hence, applying equality here ...

☣ A+B/2 = 2x +y
☣ A-B/2 = x-2y

☣ A+B=4x+2y
☣ A-B=2x-4y

☣ ADDITION OF ABOVE TWO EQUATIONS YIELD THE VALUES OF A AND B RESPECTIVELY ...

☣ A= 3x-y and B= x+3y

☣ HENCE , THE EQUATION REDUCES TO

☣ SIN ( 3x-y) + SIN ( x+3y)

☣ which results in earlier equation

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