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Standard Valu...

Standard Values

Trending Questions

Q.

Find the value of $\tan 40^{0}$ .

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Q. If the value of

2 s i n 2 θ = \sqrt{3}

, then the value of

θ

is ______.

$45^{\circ}$
$30^{\circ}$
$60^{\circ}$
$90^{\circ}$

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Q.

Prove that $sin 80^{\circ} cos 10^{\circ}$ + $cos 80^{\circ} s i n 10^{\circ}$ = 1

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Q.

What is cos $45^{\circ}$ sin $45^{\circ}$ ..............

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Q. Question 4
If

s i n θ = \frac{a}{b}

, then

c o s θ

is equal to

(A)

\frac{b}{\sqrt{b^{2} - a^{2}}}

(B)

\frac{b}{a}

(C)

\frac{\sqrt{b^{2} - a^{2}}}{b}

(D)

\frac{a}{\sqrt{b^{2} - a^{2}}}

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Q.

Area(in $c m^{2}$ ) of the sector of angle $60^{\circ}$ of a circle with radius 10 cm is

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52 "]' style="font-size:13px;font-family:arial, sans, sans-serif;">
52 "]' style="font-size:13px;font-family:arial, sans, sans-serif;">
52 "]' style="font-size:13px;font-family:arial, sans, sans-serif;">

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Q.

In an equilateral triangle ABC, the ratio of length of the perpendicular AD to side AB is

1/2
√3/2
√2
√3

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Q.

ABCD is a rhombus of side 20 cm and has two angles of $60^{\circ}$ each. The length of the diagonal AC is:

10 cm
20 cm
15 cm
None of these

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Q.

In the given figure, ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is _________.

$\sqrt{2} : 1 : 1$
$1 : 1 : \sqrt{2}$
$\sqrt{3} : 2 : 1$
$1 : 2 : \sqrt{3}$

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Q. Question 1 (iv)
Evaluate :

c o s e c 31^{\circ} - s e c 59^{\circ}

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Q. Question 1 (v)
Evaluate the following:
(v)

\frac{5 c o s^{2} 60^{\circ} + 4 s e c^{2} 30^{\circ} - t a n^{2} 45^{\circ}}{s i n^{2} 30^{\circ} + c o s^{2} 30^{\circ}}

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Q.

If sin B = 1, find the value of B if $0 \leq B \leq 90$ .

60
90
0
45

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Q. Question 1 (iv)
Evaluate the following:
(iv)

\frac{(s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ})}{(s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ})}

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Q. Question 4 (iv)
State whether the following are true or false. Justify your answer.
(iv)

s i n θ = c o s θ

for all values of

θ

.

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Q. Question 3
If tan (A + B) =

\sqrt{3}

and tan (A - B) =

\frac{1}{\sqrt{3}}

;

0^{\circ} < A + B \leq 90^{\circ}; A > B

, find A and B.

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Q.

Evaluate each of the following

sin $60^{\circ}$ cos $30^{\circ}$ + cos $60^{\circ}$ sin $30^{\circ}$

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Q. Question 1 (ii)
Evaluate the following:
(ii)

2 t a n^{2} 45^{\circ} + c o s^{2} 30^{\circ} - s i n^{2} 60^{\circ}

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Q. Value of

θ

if sin

(θ + 36^{\circ}) = cos θ

, where

θ + 36^{\circ}

is an acute angle, is

$90$ $^{\circ}$
$36$ $^{\circ}$
$54$ $^{\circ}$
$27$ $^{\circ}$

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Q.

In triangle ABC, right angled at B, if one angle is $45^{\circ}$ , find the value of sin A and cos C.

2, 2
$\frac{1}{\sqrt{2}}$ , $\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$ , $\frac{1}{\sqrt{3}}$
1, 1

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Q.

Find the acute angle $(θ)$ at which $s i n θ$ and $t a n θ$ are equal?

$30^{\circ}$
$90^{\circ}$
$0^{\circ}$
$45^{\circ}$

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Q.

If cos 3 $θ$ = $\sqrt{3}$ /2; 0 < $θ$ < 200, then value of $θ$ is:

12 degrees
0 degrees
15 degrees
10 degrees

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Q. At

θ = 90^{\circ}

which of the following trigonometric ratios are not defined?

$c o t θ, s i n θ$
$t a n θ, s e c θ$
$t a n θ, c o s e c θ$
$c o t θ, t a n θ$

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Q.

Two ships are sailing on either sides of a lighthouse. The angle of elevation of the top of the lighthouse, as observed from the ships, are 60° and 45°, respectively. If the lighthouse is 200 m tall, find the distance between the two ships. (Assume √("3" ) = 1.732)

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Q. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

(i)

{(cosec θ - cot θ)}^{2} = \frac{1 - cos θ}{1 + cos θ}

(ii)

\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A

(iii)

\frac{tan θ}{1 - cot θ} + \frac{cot θ}{1 - tan θ} = 1 + sec θ cosec θ

[Hint: Write the expression in terms of

sin θ

and

cos θ

(iv)

\frac{1 + sec A}{sec A} = \frac{{sin}^{2} A}{1 - cos A}

[Hint: Simplify LHS and RHS separately].

(v)

\frac{cos A - sin A - 1}{cos A + sin A + 1} = cosec A + cot A

, Using the identity

{cosec}^{2} A = 1 + {cot}^{2} A

(vi)

\sqrt{\frac{1 + sin A}{1 - sin A}} = sec A + tan A

(vii)

\frac{sin θ - 2 {sin}^{3} θ}{2 {cos}^{3} θ - cos θ}

(viii)

{(sin A + cosec A)}^{2} + {(cos A + sec A)}^{2} = 7 + {tan}^{2} A + {cot}^{2} A

(ix)

(cosec A - sin A) (sec A - cos A) = \frac{1}{tan A + cot A}

[Hint: Simplify LHS and RHS separately]

(x)

(\frac{1 + {tan}^{2} A}{1 + {cot}^{2} A}) = {(\frac{1 - tan A}{1 - cot A})}^{2} = {tan}^{2} A

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Q.

In a rectangle ABCD, AB = 20 cm, $∠$ BAC = $60^{\circ}$ . Then, side BC =

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Q. ABC is a right angled triangle.
If

α = 30^{\circ}

and AC = 10 cm then find the length of side BC in cm.

5

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Q.

If a triangle has angles $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ , what is the ratio of the sides of the triangle opposite to these angles respectively?

$1 : 1 : \sqrt{2}$
$\sqrt{2} : 1 : 1$
$\sqrt{3} : 2 : 1$
$1 : 2 : \sqrt{3}$

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Q. If

sin θ_{1} + sin θ_{2} + sin θ_{3} = 3,

then

cos θ_{1} + cos θ_{2} + cos θ_{3}

is equal to

$3$
$2$
$0$
$1$

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Q.

In the given figure, ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is _________.

$\sqrt{3} : 2 : 1$
$1 : 2 : \sqrt{3}$
$\sqrt{2} : 1 : 1$
$1 : 1 : \sqrt{2}$

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Q.

The diagonal of a rectangular field is $60 m e t r e s$ more than the shorter side. If the longer side is $30 m e t r e s$ more than the shorter side, find the sides of the field.

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