Question

without using trigonometric table solve the following:sin 65 ° /cos 25 ° + cos 32° / sin 58° - sin28°.sec 62° + cosec^2 30°

Answer 1

before solving this we must know that concept of complementary angles

sinx=cos 90-x  , sec x=cosec 90-x and tan x=cot 90-x

therefore ,
sin65=cos25 and cos 32=sin 58
so,
1+1-sin28(1/cos62)+cosec^2 30(sin28=cos 62)
2-(1+{1+cot^2 30})(we know that cosec^2 a=1+cot^2 a)
2-2-cot^2 30
cot^2 30 is the answer