The value of cos1° sin89° + cos2° sin88° + cos3° sin87° + …. + cos89° sin1°, is

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38 vote

The value of cos1° sin89° + cos2° sin88° + cos3° sin87° + …. + cos89° sin1°, is

Asked on 2019-07-02 23:36:41 by Guest | Votes 38 | Views: 399 | Tags: trigonometry | quantitative aptitude | Add Bounty

The value of cos1° sin89° + cos2° sin88° + cos3° sin87° + …. + cos89° sin1°, is

1). 0
2). 1
3). 44.5
4). 45

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1 answers

21 vote

Answered by Guest on 2019-07-02 23:42:25 | Votes 21 | #

Sin (90 – x) = cosx

sin 89° can be written as sin 1° and all the rest can be written in the same way

⇒ cos²(1) + cos²(2) +?+ cos²(89) can be grouped as

⇒ cos²(1) + cos²(90 − 1) + cos²(2) + cos²(90 − 2) +?+ cos²(44) + cos²(90−44) + cos²(45)

⇒ (cos²(1) + sin²(1)) + (cos²(2) + sin²(2)) +?+ (cos²(44) + sin²(44)) + cos²(45)

⇒ 44 + (1 / 2) = 44.5

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