S=sin²2+sin4²+sin6²+..........+sin²90 ,then the value of S is
VRG:
THe question is confusing. Is it sin^2 4 or sin 4^2?
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As you know, sin²x + cos²x = 1 and sin(x) = cos(90-x)
So, sin²46 = cos²(90-46) = cos²(44)
Similarly, sin²48 = cos²42...
Now, we have sin²2 + sin²4 + sin²6 + ... + sin²44 + cos²44 + cos²42 + cos²40 + ... + cos²2 + cos²0.
Pairing sin²2 and cos²2, sin²4 and cos²4, ... , sin²44 and cos²44, we get 1+1+1...+1 and cos²0 = 1
So, ultimately we get 22 ones and cos²90=1 so we get 23 ones.
Therefore the answer = 23.
So, sin²46 = cos²(90-46) = cos²(44)
Similarly, sin²48 = cos²42...
Now, we have sin²2 + sin²4 + sin²6 + ... + sin²44 + cos²44 + cos²42 + cos²40 + ... + cos²2 + cos²0.
Pairing sin²2 and cos²2, sin²4 and cos²4, ... , sin²44 and cos²44, we get 1+1+1...+1 and cos²0 = 1
So, ultimately we get 22 ones and cos²90=1 so we get 23 ones.
Therefore the answer = 23.
class 10. lives in meerut
Ah...
studying at DMA
coaching at FIITJEE meerut
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where do you live
Bangalore
omg
engineering at where
PES University
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