Question

Please solve 106.dont simply chose option.

Answer 1

sin²2+sin²4+........+sin²44+sin²46+........+sin²86+sin²88+sin²90

= sin²2+sin²4+.......+sin²44+cos²44+.......+cos²4+cos²2+1

Likewise, all terms except sin²90 will be paired with their cosines (22 times)

= 22+1= 23 (B)

ELABORATION:-

We know, sin²A+cos²A=1 and cos A= sin(90-A)

Now,

Every angle after 44 degree will start in its cos form from 44 to 2.

(sin 46 = cos(90-46)= cos 44)

Thus the angles will get paired 22 times to produce 22*1 = 22 as result. Now, sin²90 is not paired but we know its value to be 1.

Hence answer= 22+1=23