Question

sin square5° + sin square6° + sin square7° +.........+ sin square 85°
(a) 10.5
(b) 40.5
(c) 1
(d) 38​

Answer 1

Answer:

b) 40.5

Step-by-step explanation:

we know , sin²5° + sin²85° = 1

cause:- sin²85° = cos²5° [ complementary angles of trigonometric ratios ]

And , sin²5° + cos²5° = 1.

continuing this process from 6° to 44° from left and from 84° to 46° from right ....we get

40.

and sin²45° is left in the middle ..

=>sin²45°= (1/√2)²

=>1/2= 0.5

therefore, adding this to 40 , we get 40.5.

Hope it helped !!

Thanks !!!