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secondary 3 | A Maths
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Trigonometry identities
Date Posted: 3 years ago
Views: 256
1 - a tan θ = sec θ
1 - a sin θ / cos θ = 1 / cos θ
Multiply throughout by cos θ,
cos θ - a sin θ = 1
a sin θ = 1 - cos θ
a = (1 - cos θ) / sin θ
b - cot θ = cosec θ
b - cos θ / sin θ = 1 / sin θ
b = 1 / sin θ + cos θ / sin θ
b = (1 + cos θ) / sin θ
Then,
ab = (1 - cos θ) / sin θ × (1 + cos θ) / sin θ
ab = (1 - cos θ)(1 + cos θ) / sin² θ
ab = (1² - cos²θ) / sin² θ
ab = sin² θ / sin² θ
ab = 1
1 - a sin θ / cos θ = 1 / cos θ
Multiply throughout by cos θ,
cos θ - a sin θ = 1
a sin θ = 1 - cos θ
a = (1 - cos θ) / sin θ
b - cot θ = cosec θ
b - cos θ / sin θ = 1 / sin θ
b = 1 / sin θ + cos θ / sin θ
b = (1 + cos θ) / sin θ
Then,
ab = (1 - cos θ) / sin θ × (1 + cos θ) / sin θ
ab = (1 - cos θ)(1 + cos θ) / sin² θ
ab = (1² - cos²θ) / sin² θ
ab = sin² θ / sin² θ
ab = 1
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