Question

sin ²1°+sin ²3°+....+sin ²87°+sin ²89° =?

Answer 1

Answer:

sinx=cos(90-x)

=> sin89=cos(90-89)= cos1°

therefore by the equation sin^2(x)+cos^2(x)=1

[ we can find how many terms are there by using AP, 89=a+(n-1)d

89=1+(n-1)2

88/2=n-1

n=45

]

therefore only sin45 remains after using the above equation

therefore the answer will be

$22 + (1 \div \sqrt{2)}$