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Question

The value of 12tan585+sec(660)+sin405cot510cosec (570) is

A
5232
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B
3232
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C
12+32
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D
1232
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Solution

The correct option is D 1232
12tan585+sec(660)+sin405cot510cosec (570)

We know that,
tan585=tan(720585)=tan135=1sec(660)=sec(660)=sec(720660)=sec60=2sin405=sin(360+45)=sin45=12cot510=cot(360+150)=cot150=3cosec (570)=cosec (570)=cosec (720570)=cosec (150)=2

Now, putting the values in the expression, we get
12tan585+sec(660)+sin405cot510cosec (570)=12+212×32=12+2322=1232

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