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

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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 –

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Important Questions on Properties of Triangles

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IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 49

If

a, b, c

be the sides of a triangle

A B C

and if roots of equation

a (b - c) x^{2} + b (c - a) x + c (a - b) = 0

are equal, then

\sin^{2} \frac{A}{2}, \sin^{2} \frac{B}{2}, \sin^{2} \frac{C}{2}

are in

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 50

In a

Δ ABC, b^{2} + c^{2} = 1999 a^{2}

, then

\frac{\cot B + \cot C}{\cot A} =

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 51

Positive integers

a, b

and

c

are the sides of

∆ A B C

opposite to angles

A, B, C

respectively and

\frac{2}{1! 9!} + \frac{2}{3! 7!} + \frac{1}{5! 5!} = \frac{2^{a}}{b!}

. Also

a, b, c

are in A.P., then

\sin A : \sin C =

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 52

In

∆ A B C

if

{(1 + a x)}^{b} = 1 + 8 x + 24 x^{2} + \dots, b \in N

, and

\sin^{100} C - \cos^{100} C = 1

, then find the ratio of

a : b : c =

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 53

In a

Δ A B C, a

and

b

are positive integers such that

\frac{2}{1! 9!} + \frac{2}{3! 7!} + \frac{1}{5! 5!} = \frac{2^{a}}{b!}

and the distance of a variable point on the curve

x^{2} - x y + y^{2} = 10

from the origin is

r

and

c

is the maximum value of

r^{2}

, then

∆ A B C

is necessarily

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 54

If there are only two linear functions

f

and

g

which map

[1, 2]

on

[4, 6]

and in a

∆ A B C, c = f (1) + g (1)

and

a

is the maximum value of

r^{2}

, where

r

is the distance of a variable point on the curve

x^{2} + y^{2} - x y = 10

from the origin, then

\sin A : \sin C

is

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TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 55

A point

P (x, y)

in the

x y

-plane is called a lattice point if

x, y \in I

and

a

and

b

are the number of lattice points in the interior of the circles

x^{2} + y^{2} = 2

and

x^{2} + y^{2} = 3

respectively and

a, b, c

are in

A . P .

, then

c =

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IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 56

If equations

a x^{2} + b x + c = 0

and

4 x^{2} + 5 x + 6 = 0

have a common root, where

a, b, c

are the sides of

∆ A B C

, opposite to angles

A, B, C

respectively, then

2 A =