Trig Ratios

If cos θ + sin θ = √2 cos θ, then cos θ - sin θ is:

If a cos θ - b sin θ = c, then a sin θ + b cos θ is:

What is the value of 1 / (1 + sin²θ) + 1 / (1 + cosec²θ)?

If sin θ + cosec θ = 2, then find sinⁿ θ + cosecⁿ θ.

Find the value of (1 + tan θ + sec θ)(1 + cot θ - cosec θ).

Evaluate: sin⁶θ + cos⁶θ + 3 sin²θ cos²θ

If 5 sin θ = 3, find the value of (sec θ - tan θ) / (sec θ + tan θ).

If tan A + tan B = a and cot A + cot B = b, then cot(A+B) is:

If sec θ = x + 1/(4x), then find sec θ + tan θ.

If x = a cos θ and y = b sin θ, find (x²/a² + y²/b²).

Evaluate: tan 1° tan 2° tan 3° ... tan 89°.

If sin θ - cos θ = 0, find the value of sin⁴θ + cos⁴θ.

The maximum value of sin θ * cos θ is:

If x sin³θ + y cos³θ = sin θ cos θ and x sin θ = y cos θ, then x² + y² is:

Find the value of cos²θ(1 + tan²θ).

If cosec θ - cot θ = p, find the value of cos θ.

Simplify: √((1 - cos θ) / (1 + cos θ))

If 2 sin θ = 3 cos θ, find the value of sin θ.

Find the value of (sin θ / (1 - cot θ)) + (cos θ / (1 - tan θ)).

If m = tan θ + sin θ and n = tan θ - sin θ, find m² - n².