Find the value of the following: 
 \(\left( \frac { cos47° }{ sin43° } \right) +\left( \frac { sin72° }{ cos18° } \right) -2\cos^{ 2 }45°\)

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.

Verify the following equalities :
1+ tan²30⁰ = sec²30⁰

Verify the following equalities :
cos 90⁰ = 1- 2sin²45⁰ = 2cos²45⁰-1

Verify the following equalities :
sin 30°cos 60°+ cos 3°sin 60° = sin 90°