Find the sum of-sin 2 1-sin 2 2-sin 2 3-sin 2 4-sin 2 89-sin 2 90-

The correct option is B 45.5sin^2 89^∘ = cos^2 1^∘ Similarlry sin^2 88^∘ = cos^2 2^∘ sin^2 1^∘ + sin^2 89^∘ = sin^2 1^∘ + cos^2 1^∘ = 1 Similarly, sin^2 2^∘ + ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

Find the sum ...

Question

Find the sum of:
$s i n^{2} 1^{\circ} + s i n^{2} 2^{\circ} + s i n^{2} 3^{\circ} + s i n^{2} 4^{\circ} + . . . . . . . . . . s i n^{2} 89^{\circ} + s i n^{2} 90^{\circ}$

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45.5

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44.5

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Solution

The correct option is B
45.5

$s i n^{2} 89^{\circ} = c o s^{2} 1^{\circ}$
$S i m i l a r l r y s i n^{2} 88^{\circ} = c o s^{2} 2^{\circ}$
$s i n^{2} 1^{\circ} + s i n^{2} 89^{\circ} = s i n^{2} 1^{\circ} + c o s^{2} 1^{\circ} = 1$
$S i m i l a r l y, s i n^{2} 2^{\circ} + s i n^{2} 88^{\circ} = s i n^{2} 2^{\circ} + c o s^{2} = 1$
$T h e r e a r e 44 p a i r s l i k e t h i s a n d s i n^{2} 45^{\circ} = \frac{1}{2}, s i n^{2} 90^{\circ} = 1$
$S o t h e r e q u i r e d s u m i s 44 + \frac{1}{2} + 1 = 45.5$

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Similar questions

The value of ${sin}^{2} 1^{\circ} + {sin}^{2} 2^{\circ} + {sin}^{2} 2^{\circ} + . . . + {sin}^{2} 89^{\circ} + {sin}^{2} 90^{\circ}$

Q. Prove that:
(i) sin 38° + sin 22° = sin 82°
(ii) cos 100° + cos 20° = cos 40°
(iii) sin 50° + sin 10° = cos 20°
(iv) sin 23° + sin 37° = cos 7°
(v) sin 105° + cos 105° = cos 45°
(vi) sin 40° + sin 20° = cos 10°

$\frac{c o s 22^{\circ} - s i n 22^{\circ}}{c o s 22^{\circ} + s i n 22^{\circ}}$ equal to tanA, $0^{\circ}$ < A < $90^{\circ}$ . Find the value of A.

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Q. Find value of:

\frac{c o s 67}{s i n 23}

$s i n^{2} 1 + s i n^{2} 89 + c o s^{2} 7 + c o s^{2} 83 = ?$

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Find the sum of: sin2 1∘+sin2 2∘+sin2 3∘+sin2 4∘+..........sin2 89∘+sin2 90∘

The correct option is B 45.5sin2 89∘=cos2 1∘ Similarlry sin2 88∘=cos2 2∘ sin2 1∘+sin2 89∘=sin2 1∘+cos2 1∘=1 Similarly, sin2 2∘ +sin2 88∘=sin2 2∘+cos2=1 There are 44 pairs like this and sin2 45∘=12,sin2 90∘=1 So the required sum is 44+12+1=45.5

Find the sum of:
$s i n^{2} 1^{\circ} + s i n^{2} 2^{\circ} + s i n^{2} 3^{\circ} + s i n^{2} 4^{\circ} + . . . . . . . . . . s i n^{2} 89^{\circ} + s i n^{2} 90^{\circ}$