TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 40

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Mathematics

IMPORTANT

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A circle is inscribed in an equilateral triangle of side $' a' cm$ . The area (in ${cm}^{2}$ ) of a square inscribed in the circle is

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Important Questions on Properties of Triangles

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 41

Let

A_{0} A_{1} A_{2} A_{3} A_{4} A_{5}

be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments

A_{0} A_{1}, A_{0} A_{2}

and

A_{0} A_{4}

is:

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 42

If

A_{1} A_{2} A_{3} \dots A_{n}

be a regular polygon of

n

sides and

\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}}

, then

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 43

In a triangle

A B C,

\tan A + \tan B + \tan C = 10

then the triangle is

EASY

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IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 44

In a triangle

A B C, \sqrt{a} + \sqrt{b} - \sqrt{c}

is

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IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 45

In any triangle

A B C

, the least value of

\frac{\sin^{2} A + \sin A + 1}{\sin A}

is

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IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 46

Let

f (x + y) = f (x) \cdot f (y)

for all

x

and

y

and

f (1) = 2 .

If in a triangle

A B C

,

a = f (3), b = f (1) + f (3), c = f (2) + f (3)

, then

2 A =

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 47

In a triangle

A B C

, the angle

B

is greater than angle

C

. If the measure of angles

B

and

C

satisfy the equation

4 \sin^{3} x - 3 \sin x + 0.75 = 0

, then the measure of angle

A

is

EASY

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 48

In a triangle $A B C, ∠ B = \frac{π}{3} and ∠ C = \frac{π}{4} .$ Let D divides BC internally in the ratio 1: 3, then $\frac{\sin ∠ B A D}{\sin ∠ C A D}$ is equal to –