Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions
∑ r =116√1+co...
Question
∑16r=1√1+cos4r =(where 'r' is in degrees)
A
4√2sin1∘cos2∘cos17∘
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B
4√2cos1∘cos2∘cos17∘
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C
4√2cos1∘sin2∘cos17∘
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D
√2sin16∘cos17∘sin1∘
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Solution
The correct option is D√2sin16∘cos17∘sin1∘ ∑16r=1√1+cos4r=∑16r=1√2cos2r=√2(cos2∘+cos4∘+cos6∘+....+cos32∘)=√2sin16∘sin1∘cos{2+(15)(1)}=√2sin16∘cos17∘sin1∘