Evaluate cos220 - - cos270 -sin220 - - sin270 - - sin 264 - - cos64 -sin26 -

cos^220^∘+cos^270^∘sin^220^∘+sin^270^∘+sin^264^∘+cos64^∘sin26^∘ =cos^220^∘+cos^2(90^∘ 20^∘)sin^220^∘+sin^2(90^∘ 20^∘)+sin^264^∘+cos64^∘sin(90^∘ 64^∘) ...

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Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

Evaluate co...

Question

Evaluate $\frac{{cos}^{2} 20^{\circ} + {cos}^{2} 70^{\circ}}{{sin}^{2} 20^{\circ} + {sin}^{2} 70^{\circ}} + {sin}^{2} 64^{\circ} + cos 64^{\circ} sin 26^{\circ}$

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Solution

$\frac{{cos}^{2} 20^{\circ} + {cos}^{2} 70^{\circ}}{{sin}^{2} 20^{\circ} + {sin}^{2} 70^{\circ}} + {sin}^{2} 64^{\circ} + cos 64^{\circ} sin 26^{\circ}$
$= \frac{{cos}^{2} 20^{\circ} + {cos}^{2} (90^{\circ} - 20^{\circ})}{{sin}^{2} 20^{\circ} + {sin}^{2} (90^{\circ} - 20^{\circ})} + {sin}^{2} 64^{\circ} + cos 64^{\circ} sin (90^{\circ} - 64^{\circ})$
$= \frac{{cos}^{2} 20^{\circ} + {sin}^{2} 20^{\circ}}{{sin}^{2} 20^{\circ} + {cos}^{2} 20^{\circ}} + {sin}^{2} 64^{\circ} + cos 64^{\circ} cos 64^{\circ}$
$= \frac{1}{1} + {sin}^{2} 64^{\circ} + {cos}^{2} 64^{\circ}$
$= 1 + 1 = 2$

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Similar questions

\frac{{c o s}^{2} 20^{\circ} + {c o s}^{2} 70^{\circ}}{{s i n}^{2} 31^{\circ +} + {s i n}^{2} 59^{\circ}} + {s i n}^{2} 64^{\circ} + c o s 64^{\circ} s i n 26^{\circ}

Q. Evaluate:

\frac{{cos}^{2} 20 + {cos}^{2} 70}{{sin}^{2} 59 + {sin}^{2} 31}

Without using tables, evaluate :
$\frac{{cos}^{2} 20^{\circ} + {c o s}^{2} 70^{\circ}}{{s i n}^{2} 59^{\circ} + {s i n}^{2} 31^{\circ}}$

Q. Evaluate:

\frac{{sin}^{2} 63^{o} + {sin}^{2} 27^{o}}{{cos}^{2} 17^{o} + {cos}^{2} 73^{o}}

Q. Evaluate:

{lim}_{x \to π} \frac{{sin}^{2} x + {cos}^{2} x}{{sin}^{2} x - {cos}^{2} x}

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Evaluate cos220∘+cos270∘sin220∘+sin270∘+sin264∘+cos64∘sin26∘

cos220∘+cos270∘sin220∘+sin270∘+sin264∘+cos64∘sin26∘=cos220∘+cos2(90∘−20∘)sin220∘+sin2(90∘−20∘)+sin264∘+cos64∘sin(90∘−64∘)=cos220∘+sin220∘sin220∘+cos220∘+sin264∘+cos64∘cos64∘=11+sin264∘+cos264∘=1+1=2

Evaluate $\frac{{cos}^{2} 20^{\circ} + {cos}^{2} 70^{\circ}}{{sin}^{2} 20^{\circ} + {sin}^{2} 70^{\circ}} + {sin}^{2} 64^{\circ} + cos 64^{\circ} sin 26^{\circ}$