if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

(a)

\(\frac { 1 }{ 2 } \)

(b)

0

(c)

sin90°

(d)

cos90°

If tan \(\theta\) cot 37⁰ , then the value of \(\theta\) is ________.

(a)

37⁰

(b)

53⁰

(c)

90⁰

(d)

1⁰

The value of tan72° tan18° is ________.

(a)

0

(b)

1

(c)

18⁰

(d)

72⁰

The value of \(\frac { tan15° }{ cot75° } \) is

(a)

cos 90⁰

(b)

sin 30⁰

(c)

tan 45⁰

(d)

cos 30⁰

if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos³ \(\alpha\)) is equal to

(a)

0

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

-1

The value of 3 sin 70⁰sec 20⁰ + 2 sin 49⁰sec 51⁰ is ________.

(a)

2

(b)

3

(c)

5

(d)

6

The value of \(\frac { 1-{ tan }^{ 2 }{ 45 }^{ 0 } }{ 1+{ tan }^{ 2 }{ 45 }^{ 0 } } \) is ________.

(a)

2

(b)

1

(c)

0

(d)

\(\frac { 1 }{ 2 } \)

The value of cosec(70⁰ + \(\theta\)) - sec(20⁰ - \(\theta\)) + tan(65⁰ + \(\theta\)) - cot(25⁰ - \(\theta\)) is ________.

(a)

0

(b)

1

(c)

2

(d)

3

The value of tan 1° tan 2° tan 3°...tan 89° is ________.

(a)

0

(b)

1

(c)

2

(d)

\(\frac { \sqrt { 3 } }{ 2 } \)

Given that sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and cos \(\beta\) = \(\frac { 1 }{ 2 } \), then the value of \(\alpha\) + \(\beta\) is ________.

(a)

0⁰

(b)

90⁰

(c)

30⁰

(d)

60⁰

The value of \(\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' } \) is

(a)

0

(b)

2

(c)

1

(d)

-1

From the given figure, find the values of 
(i) sin B
(ii) sec B
(iii) cot B  
(iv) cos C
(v) tan C
(vi) cosec C

If 2cos \(\theta\) = \(\sqrt { 3 } \), then find all the trigonometric ratios of angle \(\theta\)

If cos A = \(\frac { 2x }{ 1+{ x }^{ 2 } } \) then find the values of sinA and tan A in terms of x.

If 3 cot A = 2 , then find the value of = \(\frac { 4\ sin\ A-3\ cos\ A }{ 2\ sin\ A+3\ cos\ A } \)

From the given figure, prove that \(\theta +\phi =90°\) Also prove that there are two other right angled triangles. Find sin \(\alpha\), cos\(\beta\) and tan\(\phi \)   

Verify the following equalities :
sin²60⁰ + cos²60⁰ = 1

Verify 3 cos A = 4 cos³ A - 3 cosA , when A = 30⁰

Find the value of 8 sin 2x cos 4x sin 6x , when x =15⁰

Find the area of a right triangle whose hypotenuse is 10cm and one of the acute angle is 24⁰24'

In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree  measures 42° and the distance to the tree is 60 metres. Find the height of the tree.

For the measures in the figure, compute sine, cosine and tangent ratios of the angle \(\theta \)

If tan A  = \(\frac { 2 }{ 3 } \) , then find all the other trigonometric ratios.

Find the value of sin 64⁰34'.

Find the values of the following:
(i) (cos 0⁰ + sin 45⁰ + sin 30⁰)(sin 90⁰ - cos 45⁰ + cos 60⁰)
(ii) tan²60⁰ - 2tan²45⁰ - cot²30⁰ +2sin²30⁰ + \(\frac { 3 }{ 4 } \) cosec² 45⁰

Find the value of \(\theta\) if
(i) sin \(\theta\) = 0.9858
(ii) cos\(\theta\) = 07656