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Trigonometric Functions

Multiple Choice Questions

What is the value of $\frac{\sin (34 °) \cos (236 °) - \sin (56 °) \sin (124 °)}{\cos (28 °) \cos (88 °) + \cos (178 °) \sin (208 °)}$ = ?

$\tan (54 °) can be expressed as$

$\frac{\sin (9 °) + \cos (9 °)}{\sin (9 °) - \cos (9 °)}$
$\frac{\sin (9 °) - \cos (9 °)}{\sin (9 °) + \cos (9 °)}$
$\frac{\cos (9 °) + \sin (9 °)}{\cos (9 °) - \sin (9 °)}$
$\frac{\sin (36 °)}{\cos (36 °)}$

3.
If p = $Xcos (θ) - Ysin (θ)$ , q = $Xsin (θ) + Ycos (θ)$ and p² + 4pq + q² = AX² + BY², $0 \leq θ \leq \frac{π}{2}$ . What is the value of $θ$ ?

$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$

$\frac{π}{4}$

$p = X \cos (θ) - Y \sin (θ) q = X \sin (θ) + Y \cos (θ) p^{2} = X^{2} \cos^{2} (θ) + Y^{2} \sin^{2} (θ) - 2 XYsin (θ) \cos (θ) q^{2} = X^{2} \sin^{2} (θ) + Y^{2} \cos^{2} (θ) + 2 XYsin (θ) \cos (θ) p^{2} + q^{2} = X^{2} (\sin^{2} (θ) + \cos^{2} (θ)) + Y^{2} (\sin^{2} (θ) + \cos^{2} (θ)) p^{2} + q^{2} = X^{2} + Y^{2} pq = (Xcos (θ)) (Ysin (θ)) + (Xcos (θ)) (Ycos (θ)) - (Ysin (θ)) (Xsin (θ)) - (Y \sin (θ)) (Ycos (θ)) pq = X^{2} \sin (θ) \cos (θ) + {XYcos}^{2} (θ) - XY \sin^{2} (θ) - Y^{2} \sin (θ) \cos (θ) 4 pq = 2 X^{2} \sin (2 θ) - 2 Y^{2} \sin (2 θ) + 4 XYcos (2 θ) p^{2} + q^{2} + 4 pq = X^{2} (1 + 2 \sin (2 θ)) Compare with {AX}^{2} + {BY}^{2} We get, A = 1 + 2 \sin (2 θ) B = 1 - 2 \sin (2 θ) 4 XYcos (2 θ) = 0$

$∵ XY \neq 0 ∴ \cos (2 θ) = 0 \cos (2 θ) = \cos (\frac{π}{2}) 2 θ = \frac{π}{2} θ = \frac{π}{4} \Rightarrow 0 \leq θ \leq \frac{π}{2}$

$If p = (Xcos (θ) - Ysin (θ)), q = Xsin (θ) + Ycos (θ) and p^{2} + 4 pq + q^{2} = {AX}^{2} + {BY}^{2}, 0 \leq θ \leq \frac{π}{2}$

What is the value of A ?

$If p = (Xcos (θ) - Ysin (θ)), q = Xsin (θ) + Ycos (θ) and p^{2} + 4 pq + q^{2} = {AX}^{2} + {BY}^{2}, 0 \leq θ \leq \frac{π}{2}$

-1
0
1
2

$It is given that \cos (θ - α) = a, \cos (θ - β) = b What is \cos (α - β) = ?$

$ab + \sqrt{1 - a^{2}} \sqrt{1 - b^{2}}$
$ab - \sqrt{1 - a^{2}} \sqrt{1 - b^{2}}$
$a \sqrt{1 - b^{2}} - b \sqrt{1 - a^{2}}$
$a \sqrt{1 - b^{2}} + b \sqrt{1 - a^{2}}$

It is given that $\cos (θ - α) = a, \cos (θ - β) = b .$ $What is \sin^{2} (α - β) + 2 abcos (α - β) = ?$

a² + b²
a² - b²
b² - a²
- (a² + b²)

$If \sin (α) + \cos (α) = p, then what is \cos^{2} (2 α) = ?$

$p^{2}$
$p^{2} - 1$
$p^{2} (2 - p^{2})$
$p^{2} + 1$

$If \tan (θ) = \frac{1}{2} and \tan (φ) = \frac{1}{3}, then what is the value of (θ + ϕ)$

0
$\frac{π}{6}$
$\frac{π}{4}$
$\frac{π}{2}$

10.

$If \cos (A) = \frac{3}{4}, then what is the value of \sin (\frac{A}{2}) \sin (\frac{3 A}{2}) = ?$

$\frac{5}{8}$
$\frac{5}{16}$
$\frac{5}{24}$
$\frac{7}{32}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

3. If p = Xcosθ - Ysinθ, q = Xsinθ + Ycosθ and p2 + 4pq + q2 = AX2 + BY2, 0 ≤ θ ≤ π2. What is the value of θ ? π2 π3 π4 π6

3.
If p = $Xcos (θ) - Ysin (θ)$ , q = $Xsin (θ) + Ycos (θ)$ and p² + 4pq + q² = AX² + BY², $0 \leq θ \leq \frac{π}{2}$ . What is the value of $θ$ ?

$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$