The value of sin 2 2-sin 2 4-sin 2 6-sin 2 90- is

sin22 deg; + sin24 deg; + sin26 deg; + ... + sin290 deg; = sin22 deg; + sin24 deg; + sin26 deg; + ... + sin284 deg; + sin286 deg; + sin288 ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

The value of ...

Question

The value of sin²2° + sin²4° + sin²6° + ... + sin²90° is ____________.

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Solution

sin²2° + sin²4° + sin²6° + ... + sin²90°

= sin²2° + sin²4° + sin²6° + ... + sin²84° + sin²86° + sin²88°+ sin²90°

= [(sin²2° + sin²88°) + (sin²4° + sin²86°) + (sin²6° + sin²84°) + .... 22 pair of terms] + sin²90°

= [(sin²2° + cos²2°) + (sin²4° + cos²4°) + (sin²6° + cos²6°) + .... 22 pair of terms] + sin²90° [sin(90º − θ) = cosθ]

= (1 + 1 + 1 + ... 22 terms) + 1 [sin²θ + cos²θ = 1 and sin90° = 1]

= 22 + 1

= 23

The value of sin²2° + sin²4° + sin²6° + ... + sin²90° is 23.

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The value of sin22° + sin24° + sin26° + ... + sin290° is ____________.

The value of sin²2° + sin²4° + sin²6° + ... + sin²90° is ____________.