gys please tell me it explanation
sin ²5°+sin²6°+sin²7°+....................sin²85°=?
if you have correct answer i will mark you
and it answer is 40.5
Answers
sin^2 5 + sin^2 6 + sin^2 7 + .... + sin^2 45 + .....+ sin^2 83 + sin^2 84 + sin^2 85
Observe here, that sin 85 can be written as cos 5,
Similarly, sin 83 can be written as cos 7 , and sin 84 can be written as cos 6
Similar conversions can be done for all sin terms till 46°
And, thus 40 pairs of sin^2 and cos^2 terms are obtained
We, know sin ^2 © + cos ^2 © = 1
So, forty of those terms would give us 40 and one sin^2 45 = (1/√2)^2 = 0.5
So,
Final answer = 40+0.5 = 40.5
Answer:
sin^2 5 + sin^2 6 + sin^2 7 + .... + sin^2 45 + .....+ sin^2 83 + sin^2 84 + sin^2 85
Observe here, that sin 85 can be written as cos 5,
Similarly, sin 83 can be written as cos 7 , and sin 84 can be written as cos 6
Similar conversions can be done for all sin terms till 46°
And, thus 40 pairs of sin^2 and cos^2 terms are obtained
We, know sin ^2 © + cos ^2 © = 1
So, forty of those terms would give us 40 and one sin^2 45 = (1/√2)^2 = 0.5
So,
Final answer = 40+0.5 = 40.5