Find the value of-sin90- cos0- - sin88- cos2- - sin86- cos4- - -sin2- cos88- - sin0- cos90-

Sin90^∘ cos0^∘ + sin88^∘ cos2^∘ + ............+ sin2^∘ cos88^∘ + sin0^∘ cos90^∘ = cos(90^∘ 90^∘)cos0^∘ + cos(90^∘ 88^∘)cos2^∘ + .............+ cos(90^∘ 46^ ...

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Byju's Answer

Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

Find the valu...

Question

Find the value of:
$s i n 90^{\circ} c o s 0^{\circ} + s i n 88^{\circ} c o s 2^{\circ} + s i n 86^{\circ} c o s 4^{\circ} + . . . . . . . . . . . . . . + s i n 2^{\circ} c o s 88^{\circ} + s i n 0^{\circ} c o s 90^{\circ}$

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Solution

$s i n 90^{\circ} c o s 0^{\circ} + s i n 88^{\circ} c o s 2^{\circ} + . . . . . . . . . . . . + s i n 2^{\circ} c o s 88^{\circ} + s i n 0^{\circ} c o s 90^{\circ} = c o s (90^{\circ} - 90^{\circ}) c o s 0^{\circ} + c o s (90^{\circ} - 88^{\circ}) c o s 2^{\circ} + . . . . . . . . . . . . . + c o s (90^{\circ} - 46^{\circ}) c o s (44^{\circ}) + s i n (44^{\circ}) s i n (90^{\circ} - 46^{\circ}) + s i n (42^{\circ}) s i n (90^{\circ} - 48^{\circ}) + . . . . . . . . . . . . + s i n 0^{\circ} s i n (90^{\circ} - 90^{\circ}) = c o s 0^{\circ} c o s 0^{\circ} + c o s 2^{\circ} . c o s 2^{\circ} + . . . . . . . . . . . . + c o s 44^{\circ} c o s 44^{\circ} + s i n 44^{\circ} s i n 44^{\circ} + . . . . . . . . . . + s i n 2^{\circ} . s i n 2^{\circ} + s i n 0^{\circ} . s i n 0^{\circ} = c o s^{2} 0^{\circ} + c o s^{2} 2^{\circ} + . . . . . . . . . . . . + c o s^{2} 44^{\circ} + s i n^{2} 44^{\circ} + . . . . . . . . . . . . + s i n^{2} 2^{\circ} + s i n^{2} 0^{\circ} = 1 + 1 + 1 + . . . . . . . . . + 1 (23 t i m e s) = 23$

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s i n 90^{\circ} c o s 0^{\circ} + s i n 88^{\circ} c o s 2^{\circ} + s i n 86^{\circ} c o s 4^{\circ} + . . . . . . . . . . . . . . + s i n 2^{\circ} c o s 88^{\circ} + s i n 0^{\circ} c o s 90^{\circ}

Q. What is the value of

\frac{sin 2^{\circ} sin 4^{\circ} sin 6^{\circ} . . . . . sin 88^{\circ}}{cos 88^{\circ} cos 86^{\circ} cos 84^{\circ} . . . . . cos 2^{\circ}}

(Do not use trigonometric tables)

Evaluate

\begin{matrix} {cos}^{4} \frac{π}{16} + {sin}^{4} \frac{π}{16} - {sin}^{2} \frac{π}{16} {cos}^{2} \frac{π}{16} + {cos}^{4} \frac{3 π}{16} + {sin}^{4} \frac{3 π}{16} - {sin}^{2} \frac{3 π}{16} {cos}^{2} \frac{3 π}{16} \end{matrix}

Q. If

\frac{{cos}^{4} x}{{cos}^{2} y} + \frac{{sin}^{4} x}{{sin}^{2} y} = 1

, then

\frac{{cos}^{4} y}{{cos}^{2} x} + \frac{{sin}^{4} y}{{sin}^{2} x} = ?

Q. Value of

\frac{{sin}^{2} 20^{o} + {cos}^{4} 20^{o}}{{sin}^{4} 20^{o} + {cos}^{2} 20^{o}}

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Find the value of: sin90∘ cos0∘+sin88∘ cos2∘+sin86∘ cos4∘+..............+sin2∘ cos88∘+sin0∘ cos90∘

Find the value of:
$s i n 90^{\circ} c o s 0^{\circ} + s i n 88^{\circ} c o s 2^{\circ} + s i n 86^{\circ} c o s 4^{\circ} + . . . . . . . . . . . . . . + s i n 2^{\circ} c o s 88^{\circ} + s i n 0^{\circ} c o s 90^{\circ}$