Trigonometric Ratios Quiz

If $ an heta = rac{12}{5}$, what expression can be proved equal to $rac{7}{17}$?

If $ an heta = rac{1}{2}$, what is the value of $rac{ an heta + an^2 heta}{ an heta + 1}$?

If $rac{3 an A - 4 an^2 A}{ an A}$ = 0, what can be concluded about $ an A$?

Given $ an heta = rac{20}{21}$, how can $rac{1+ an heta}{1- an heta}$ be simplified?

If $ an heta = rac{1}{ an heta}$, which of the following statements is true?

If $ an heta = rac{1}{ an heta}$, what is $ an^2 heta$ equal to?

If $ an A = rac{3}{4}$, what expression evaluates to $rac{3}{7}$?

What is true if $ an A = rac{1}{ an A}$?

Trigonometric Ratios

If tan θ = a/b, then (sin θ - b cos θ) / (sin θ + b cos θ) = (a² - b²) / (a² + b²)
If sin θ = 13/12, evaluate (2 sin θ - 3 cos θ) / (4 sin θ - 9 cos θ)
If tan θ = 1/2, evaluate (cos θ + sin θ) / (sin θ + 1 + cos θ)
If sin α = 1/2, prove (3 cos α - 4 cos² α) = 0
If 3 cot θ = 2, prove (4 sin θ - 3 cos θ) / (2 sin θ + 6 cos θ) = 1/3
If sec θ = 17/8, prove 3 - 4 sin² θ = 3 - tan² θ / 4 cos² θ - 1
If tan θ = 20/21, prove (1 - sin θ + cos θ) / (1 + sin θ + cos θ) = 3/7
If tan θ = 1/√7, prove (cosec² θ + sec² θ) / (cosec² θ - sec² θ) = 4/3
If sin θ = 3/4, prove cosec² θ - cot² θ / sec θ - 1 = √7/3
If 3 tan A = 4, prove (i) (sec A - cosec A) / (sec A + cosec A) = 1/√7 and (ii) (1 - sin A) / (1 + cos A) = 1/2√2
If cot θ = 15/8, evaluate (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ)
In ΔABC, if ∠B = 90° and tan A = 1, prove 2 sin A cos A = 1
In rectangle ABCD, diagonal AC = 17 cm, ∠BCA = θ, sin θ = 8/17. Find (i) area of ABCD, (ii) perimeter of ABCD
If x = cosec A + cos A and y = cosec A - cos A, prove (x²/2) + (y²/2) / (x + y) = 1

Test your understanding of trigonometric ratios and identities with this quiz. It includes various proofs and evaluations based on fundamental trigonometric principles. Challenge yourself with problems involving sine, cosine, tangent, and cotangent.