What is the value of [(sin 4x + sin 4y) {(tan 2x – 2y)}]/(sin 4x – sin 4y)?
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Correct answer: D
Explanation
The correct answer is option 4 i.e. tan (2x + 2y)
[(sin 4x + sin 4y) {(tan 2x – 2y)}]/(sin 4x – sin 4y)
= [2sin{(4x + 4y)/2} cos{(4x - 4y)/2}[sin(2x - 2y)/cos(2x - 2y)]}/2cos(4x + 4y /2)sin(4x - 4y/ 2)
= [sin(2x + 2y) cos(2x - y)]/[cos(2x + 2y)sin(2x - 2y)] × [sin(2x - 2y)/cos(2x - 2y)]
= tan(2x + 2y)