Without using trigonometric tables find the values of:

cos70°/sin20° + cos57°cosec33°-2cos60°

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Solution

Here is the solution for your question,
cos 70/sin 20+cos 57 x cosec 33 - 2cos 60
We know that cos (90-x)= sinx
Therefore,cos 70=cos (90-20)=sin 20
Similarly,cos 57=cos (90-33)=sin 33

Therefore,the equation can be simplified as
sin 20/sin 20 + sin 33 x 1/sin 33 - 2 cos 60 (since, cosec 33=1/sin 33)
1+1-2 x 1/2 (since,cos 60=1/2)
= 2 -1
=1

Therefore, cos 70/sin 20 + cos 57 x cosec 33 - 2 cos 60 = 1

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