Show that cot θ = √2 + 1

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

Solution:

sin θ + cos θ = √2 sin (90° – θ)
sin θ + cos θ = √2 cos θ
dividing by sin θ

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

Solution:

7 sin² θ + 3 cos² θ = 4, 0° ≤ θ ≤ 90°
3 sin² θ + 3 cos² θ + 4 sin² θ = 4

More Solutions:

• Solve: sin2 θ + cos4 θ = cos2 θ + sin4 θ
• Solve: sec4 A (1 – sin4 A) – 2 tan2 A = 1
• Solve: (sec A – tan A)2 (1 + sin A) = 1 – sin A.
• Solve: (sec A – cosec A) (1 + tan A + cot A) = tan A sec A – cot A cosec A
• Solve: (sinA + cosA)2 + (sinA – cosA)2/sin2A – cos2A.
• Solve: 2 (sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = θ