Question
Determine the value of [(sin7x - sin5x) ÷ (cos7x +
cos5x)] - [(cos6x - cos4x) ÷ (sin6x + sin4x)]?Solution
ATQ,
ATQ, [(sin 7x - sin 5x) ÷ (cos 7x + cos 5x)] - [(cos 6x - cos 4x) ÷ (sin 6x + sin 4x)] Applying the formulas, sinC + sinD = 2sin[(C + D) /2] cos[(C - D) /2] sinC - sinD = 2cos[(C + D) /2] sin[(C - D) /2] cosC + cosD = 2cos[(C + D) /2] cos[(C - D) /2] cosC - cosD = - 2sin[(C + D) /2] sin[(C - D) /2] ⇒ [(2cos6xsinx) ÷ (2 cos6xcosx)] - [(-2 sin5xsinx) ÷ (2sin5xcosx)] ⇒ tanx + tanx = 2tanx
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