If cot θ + cos θ = m and cot θ - cos θ = n, then prove that (m² - n²)² = 16 mn.
Trigonometric Identities
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Question

If cot θ + cos θ = m and cot θ - cos θ = n, then prove that (m² - n²)² = 16 mn.

KnowledgeBoat · Accepted Answer

Given, cot θ + cos θ = m ....(i) cot θ - cos θ = n ....(ii) Adding (i) and (ii) we get, ⇒ m + n = cot θ + cos θ + cot θ - cos θ ⇒ m + n = 2 cot θ ⇒ 2 cot θ = m + n ⇒ cot θ = . ∴ tan θ = ....(iii) Subtracting (ii) from (i) we get, m - n = cot θ + cos θ - cot θ + cos θ m - n = 2 cos θ cos θ = . ∴ sec θ = ....(iv) Squaring and subtracting (iii) from (iv), Hence, proved that (m² - n²)² = 16 mn.

Mathematics

If cot θ + cos θ = m and cot θ - cos θ = n, then prove that (m² - n²)² = 16 mn.

Trigonometric Identities

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Mathematics

If cot θ + cos θ = m and cot θ - cos θ = n, then prove that (m2 - n2)2 = 16 mn.

Trigonometric Identities

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If cot θ + cos θ = m and cot θ - cos θ = n, then prove that (m² - n²)² = 16 mn.

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
2(sin⁶ θ + cos⁶ θ) - 3(sin⁴ θ + cos⁴ θ) + 1 = 0.

When 0° < θ < 90°, solve the following equation:
2 cos² θ + sin θ - 2 = 0

When 0° < θ < 90°, solve the following equation:
3 cos θ = 2 sin² θ