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

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

The value of tan72° tan18° is ________.

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

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

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

If 2 sin 2\(\theta\) = \(\sqrt { 3 } \) , them the value of \(\theta\) is ________.

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

The value of 2tan30° tan60° is

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

If cos A = \(\frac { 3 }{ 5 } \), them the value of tan A is

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

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

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

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

From the given figure, find all the trigonometric ratios of angle B.

From the given figure, find all the trigonometric ratios of angle \(\theta\)

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 = \(\frac { 3 }{ 5 } \), then find the value of \(\frac { sinA-cosA }{ 2tanA } \)

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

If sin \(\theta\)  = \(\frac { a }{ \sqrt { { a }^{ 2 }+{ b }^{ 2 } } } \) then show that b sin \(\theta\) = a cos \(\theta\)

If cos \(\theta\) : sin\(\theta\) =1: 2, then find the value of = \(\frac { 8cos\theta -2sin\theta }{ 4cos\theta +2sin\theta } \)

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\(\phi \)   

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios) 

Verify the following equalities :
sin²60⁰ + cos²60⁰ = 1

Find the value of the following:
(i) \(\frac { tan45° }{ cosec30° } +\frac { sec60° }{ cot45° } -\frac { 5sin90° }{ 2cos0° } \)
(ii) (sin 90⁰ + cos 60⁰ + cos 45⁰) \(\times\) (sin 30⁰ - cos 0⁰ +cos 45⁰)
(iii) sin²30⁰ - 2cos³60⁰ + 3tan⁴45⁰

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 value of the following:
(i) sin 49°
(ii) cos 74⁰39'
(iii) tan 54⁰26'
(iv) sin 21⁰21'
(v) cos 33⁰53'
(vi) tan 70⁰17'

Find the value of \(\theta\) if
(i) sin \(\theta\) = 0.9975
(ii) cos \(\theta\) = 0.6763
(iii) tan \(\theta\) = 0.0720
(iv) cos \(\theta\) = 0.0410
(v) tan \(\theta\) = 7.5958

Find the value of the following:
(i) sin65⁰39' + cos24⁰57' + tan10⁰10'
(ii) tan70⁰58' + cos15⁰26' - sin84⁰59'

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

Find the angle made by a ladder of length 5m with the ground, if one of its end is 4 m away from the wall and the other end is on the wall.

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 \(\theta \)

Find the six trigonometric ratios of the angle \(\theta\) using the given diagram.

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

Express
(i) sin 74° in terms of cosine
(ii) tan 12° in terms of cotangent
(iii) cosec 39° in terms of secant

Evaluate:
(i) \(\frac { sin\ 49° }{ cos\ 41° } \) 
(ii) \(\frac { sec\ 63° }{ cosec\ 27° } \)

Find the values of
(i) tan7° tan23° tan60° tan67° tan83°  
(ii) \(\frac { cos35° }{ sin55° } +\frac { sin12° }{ cos78° } -\frac { cos18° }{ sin72° } \)

(i) If cosec A = sec 34⁰, then find A
(ii) If tan B = cot 47⁰, then find B.

Find the value of tan70⁰13'

Find the value of
(i) sin 38⁰36' + tan 12⁰12'
(ii) tan 60⁰25' - cos 49⁰20'

Find the area of the right angled triangle with hypotenuse 5 cm and one of the acute angle is 48⁰30'

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