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Trigonometric Functions

Multiple Choice Questions

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

$\tan (54 °) can be expressed as$

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

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 $θ$ ?

$\frac{π}{2}$
$\frac{π}{3}$
$\frac{π}{4}$
$\frac{π}{6}$

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

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

6.
$It is given that \cos (θ - α) = a, \cos (θ - β) = b What is \cos (α - β) = ?$

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

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

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

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

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

$\cos (θ - α) = a (θ - α) = \cos^{- 1} (a) . . . (i) \cos (θ - β) = b (θ - β) = \cos^{- 1} (b) . . . (ii) Equaton (ii) - equation (i) - β + α = \cos^{- 1} (b) - \cos^{- 1} (a) α - β = \cos^{- 1} (ab + \sqrt{1 - a^{2}} \sqrt{1 - b^{2}}) \cos (α - β) = ab + \sqrt{1 - a^{2}} \sqrt{1 - b^{2}}$

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

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Test Yourself

Multiple Choice Questions

6. It is given that cosθ - α = a, cosθ - β = bWhat is cosα - β = ? ab + 1 - a21 - b2 ab - 1 - a21 - b2 a1 - b2 - b1 - a2 a1 - b2 + b1 - a2

6.
$It is given that \cos (θ - α) = a, \cos (θ - β) = b What is \cos (α - β) = ?$

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

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

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

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