If sin θ + cos θ = √2 sin(90° - θ), show that cot θ = √2 + 1.

Question

KnowledgeBoat · Accepted Answer

Given, sin θ + cos θ = sin(90° - θ) ⇒ sin θ + cos θ = cos θ Dividing both sides by sin θ ⇒ 1 + cot θ = cot θ ⇒ 1 = cot θ - cot θ ⇒ 1 = cot θ( - 1) ⇒ cot θ = Rationalizing, Hence, proved that cot θ = + 1.

Mathematics

If sin θ + cos θ = √2 sin(90° - θ), show that cot θ = √2 + 1.

Trigonometric Identities

Related Questions

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(sin A + sec A)² + (cos A + cosec A)² = (1 + sec A cosec A)².

If 7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.

If sec θ + tan θ = m and sec θ - tan θ = n, prove that mn = 1.

Mathematics

If sin θ + cos θ = √2 sin(90° - θ), show that cot θ = √2 + 1.

Trigonometric Identities

Related Questions

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:(sin A + sec A)2 + (cos A + cosec A)2 = (1 + sec A cosec A)2.

If 7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.

If sec θ + tan θ = m and sec θ - tan θ = n, prove that mn = 1.

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
(sin A + sec A)² + (cos A + cosec A)² = (1 + sec A cosec A)².

If 7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.