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Question

# Column IColumn IIa. sin(410∘−A)cos(400∘+A)+cos(410∘−A)sin(400∘+A) p. -1b. cos21∘−cos22∘2sin3∘sin1∘ is equal toq. 1c. sin(−870∘)+cosec(−660∘)+tan(−855∘)+2cot(840∘)+cos(480∘)+sec(900∘)r. 12 Which of the following is the CORRECT combination ?

A
ap,bq,cr
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B
ar,bq,cp
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C
aq,br,cp
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D
ar,bp,cq
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Solution

## The correct option is C a→q,b→r,c→pa. sin(410∘−A)cos(400∘+A)+cos(410∘−A)sin(400∘+A) =sin(410∘−A+400∘+A) =sin(810∘) =sin(4π+π2) =sinπ2 =1 b. cos21∘−cos22∘2sin3∘sin1∘ =(1−sin21∘)−(1−sin22∘)2sin3∘sin1∘ =sin22∘−sin21∘2sin3∘sin1∘ =sin3∘⋅sin1∘2sin3∘sin1∘ =12 c. sin(−870∘)+cosec(−660∘)+tan(−855∘)+2cot(840∘)+cos(480∘)+sec(900∘) =−sin(810∘+60∘)−cosec(630∘+30∘)−tan(810∘+45∘) +2cot(810∘+30∘)+cos(450∘+30∘)+sec(810∘+90∘) =−cos60∘+sec30∘+cot45∘ −2tan30∘−sin30∘−cosec 90∘ =−12+2√3+1−2√3−12−1 =−1

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