The value of sin25∘+sin210∘+sin215∘ + ..............+
sin285∘+sin290∘ is equal to
9 12
Given expression is
sin25∘+sin210∘+sin215∘+..............+sin285∘+sin290∘
We know that sin90∘=1 or sin290∘=1
Similarly, sin45∘=1√2 or sin245∘=12 and the angles are in A.P. of 18 terms. We also know that
sin285∘=[sin(90∘−5∘)]2=cos25∘
∴ From the complementary rule, we find~sin25∘+sin285∘=sin25∘+cos25∘=1
∴sin25∘+sin210∘+sin215∘+.............+sin285∘+sin290∘
=(1+1+1+1+1+1+1+1)+1+12=912