MEDIUM

Earn 100

Prove that $\sin 405 ° \cos 300 ° - \cos 420 ° \sin 585 ° = \sin 45 °$

Important Questions on Trigonometric Ratios and Identities

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

In a triangle

A B C

, the altitude

A D

and the median

A E

divide

∠ A

into three equal parts. If

B C = 28

, then the nearest integer to

A B + A C

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The approximate value of

\sin 31 °

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\sin (α + β) = 1, \sin (α - β) = \frac{1}{2}, α, β \in [0, \frac{π}{2}]

then the value of

\tan (α + 2 β) \tan (2 α + β)

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Let

A B C

be an isosceles triangle with

A B = A C

and incentre

I .

A I = 3

and the distance from

I

B C

2,

what is the square of the length of

B C ?

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The angle of the top of a vertical tower standing on a horizontal plane is observed to be

45 °

from a point A on the plane. Let

B

be the point

30 m

vertically above the point A. If the angle of elevation of the top of the tower from

B

30 °

, then the distance (in m) of the foot of the tower from the point

A

is:

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Let

A B

be a diameter of a circle and let

C

be a point on the segment

A B

such that

A C : C B = 6 : 7 .

Let

D

be a point on the circle such that

D C

is perpendicular to

A B .

Let

D E

be the diameter through

D .

[X Y Z]

denotes the area of the triangle

X Y Z,

find

\frac{[A B D]}{[C D E]}

to the nearest integer.

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Let $P = (θ : \sin θ - \cos θ = \sqrt{2} \cos θ}$ and $Q = {θ : \sin θ + \cos θ = \sqrt{2} \sin θ}$ be two sets. Then,

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The combined equation of the two diameters of a circle which divide the circle into

4

sectors is

a x^{2} + 2 h x y + b y^{2} = 0

. If the area of the bigger sector is

5

times the area of the smaller sector, then

\frac{|a + b|}{\sqrt{{(a - b)}^{2} + 4 h^{2}}} =

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Two vertical poles

A B = 15 m

and

C D = 10 m

are standing apart on a horizontal ground with points

A

and

C

on the ground. If

P

is the point of intersection of

B C

and

A D

, then the height of

P

(in

m

) above the line

A C

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\frac{\sin θ}{1 - \cot θ} + \frac{\cos θ}{1 - \tan θ} =

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Two parallel chords are drawn on the same side of the centre of a circle of radius

20 .

It is found that they subtend

60 °

and

120 °

angles at the centre of the circle, then the perpendicular distance between the chords is

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Suppose ABCDEF is a hexagon such that

A B = B C = C D = 1

and

D E = E F = F A = 2

. If the vertices

A, B, C, D, E, F

are concylic, the radius of the circle passing through them is-

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

5 \sin x = 3,

then what is the value of

\{\frac{(\sec x - \tan x)}{(\sec x + \tan x) + 5}\}

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

An ant leaves the anthill for its morning exercise. It walks

4

feet east and then makes a

160 °

turn to the right and walks

4

more feet. It then makes another

160 °

turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is the distance in feet it would have walked?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Let

A C B

be a triangle with right-angle at

C .

Let

A B = 29

units,

B C = 21

units and

A B C = θ .

Then

\cos^{2} θ - \sin^{2} θ =

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

Question Image

(II) 0 < q < 90°

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\cos 1 ° \cdot \cos 2 ° \cdot \cos 3 ° \cdot \dots . \cdot \cos 179 ° =

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\tan A + \cot A = 2

, then the value of

\tan^{4} A + \cot^{4} A =

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Let

P

be a closed polygon with

10

sides and

10

vertices (assume that the sides do not intersect except at the vertices). Let

k

be the number of interior angles of

P

that are greater than

180^{o} .

The maximum possible value of

k

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

\sin \frac{31 π}{3}

Prove that sin 405°cos 300°-cos 420°sin 585°=sin 45°

Important Questions on Trigonometric Ratios and Identities

Learn and Prepare for any exam you want !

Prove that $\sin 405 ° \cos 300 ° - \cos 420 ° \sin 585 ° = \sin 45 °$