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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §1.5 A Review of Trigonometry, #19 · Trigonometry · Identities

Complementary angles have

Complementary angles have $sin θ = cos (π /2 - θ)$ . Write $sin (s + t)$ as $cos (π /2 - s - t)$ and apply formula (4) with $π /2 - s$ instead of $s$ . In this way derive the addition formula (9).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §1.5 A Review of Trigonometry, #19

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