Sin square 5 degree plus Sin square 10 degree plus Sin square 15 degree plus..........Sin square 90 degree
since sin(x) = cos(90-x)
sin^2 0° + sin^2 90° = 1
sin^2 5° + sin^2 85° = 1
...
sin^2 45° + sin^2 45° = 1
Now, you have excluded sin^2 0, but since that's zero anyway. You have 9 pairs, plus a single 45, so the sum is 9.5
sinA=2tanA/2/1 tan.tanA/2
To calculate the value of sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°), you can use the concept of trigonometric identities.
One relevant identity states that sin^2(x) + cos^2(x) = 1. Rearranging this equation, we get sin^2(x) = 1 - cos^2(x).
Since we are dealing with sine squares, let's rewrite the given expression using the above identity:
sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°)
= [1 - cos^2(5°)] + [1 - cos^2(10°)] + [1 - cos^2(15°)] + ... + [1 - cos^2(90°)]
= [1 + 1 + 1 + ... + 1] - [cos^2(5°) + cos^2(10°) + cos^2(15°) + ... + cos^2(90°)]
Now, let's evaluate the second part of the expression, which is cos^2(5°) + cos^2(10°) + cos^2(15°) + ... + cos^2(90°). To do this, we need to apply another trigonometric identity.
The identity is cos^2(x) + sin^2(x) = 1. If we rearrange this equation, we get cos^2(x) = 1 - sin^2(x).
Using this identity, we can rewrite the second part of the expression as:
cos^2(5°) + cos^2(10°) + cos^2(15°) + ... + cos^2(90°)
= [1 - sin^2(5°)] + [1 - sin^2(10°)] + [1 - sin^2(15°)] + ... + [1 - sin^2(90°)]
= [1 + 1 + 1 + ... + 1] - [sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°)]
From the first part of the expression, we know that the sum [1 + 1 + 1 + ... + 1] is equal to 90 because there are 90 terms in the sum.
Now, we have the sum of sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°) and sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°) in simplified forms.
sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°) = 90 - [sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°)]
Since we cannot simplify it further without knowing the exact values of the individual terms, this is the final expression for the sum sin^2(5°) + sin^2(10°) + sin^2(15°) + ... + sin^2(90°).