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

The value of 2tan30° tan60° 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

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

Find the six trigo'nometric ratios of the angle 0 using the diagram

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

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

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

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