Q.22 Evaluate : ∫ sin(x + a)/cos(x - b) dx

Answer: cos(a + b)log|sec(x - b)| + xsin(a + b) + c Write x + a = (x - b) + (a + b) . Then sin(x + a) = sin(x - b)cos(a + b) + cos(x - b)sin(a + b) . I = ∫ sin(x - b)cos(a + b) + cos(x - b)sin(a + b)/cos(x - b)dx = cos(a + b)∫ tan(x - b) dx + sin(a + b)∫ dx = cos(a + b)log|sec(x - b)| + xsin(a + b) + c .

Evaluate : \(\int \frac{\sin(x + a)}{\cos(x - b)}\,dx\)

Q.22 Evaluate : \(\int \frac{\sin(x + a)}{\cos(x - b)}\,dx\)

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\cos(a + b)\log|\sec(x - b)| + x\sin(a + b) + c\)

Write \(x + a = (x - b) + (a + b)\). Then

\(\sin(x + a) = \sin(x - b)\cos(a + b) + \cos(x - b)\sin(a + b)\).

\(I = \int \frac{\sin(x - b)\cos(a + b) + \cos(x - b)\sin(a + b)}{\cos(x - b)}dx = \cos(a + b)\int \tan(x - b)\,dx + \sin(a + b)\int dx\)

\(= \cos(a + b)\log|\sec(x - b)| + x\sin(a + b) + c\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Evaluate : \(\int \frac{\sin(x + a)}{\cos(x - b)}\,dx\)

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