-1-4- -root3 cos 23-o - sin 23-o- -

Explanation for the correct option:Given, 1/4[√ 3 cos 23° sin 23°]=1/2[√ 3 cos 23°/2 1.sin 23°/2]=1/2[(√ 3/2)cos 23° – (1/2) sin 23°]=1/2[cos30°cos23° sin30 ...

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Byju's Answer

Standard XI

Mathematics

Solution of Triangle

(1/4) [root3 ...

Question

$\frac{1}{4} [\sqrt 3 \cos 23 ° - \sin 23 °] =$

$\cos 43 °$

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$\cos 7 °$

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$\cos 53 °$

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$N o n e o f t h e s e$

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Solution

The correct option is D
$N o n e o f t h e s e$

Explanation for the correct option:
Given, $\frac{1}{4} [\sqrt 3 \cos 23 ° - \sin 23 °]$
$= \frac{1}{2} [\frac{\sqrt 3 \cos 23 °}{2} - \frac{1 . \sin 23 °}{2}]$
$= \frac{1}{2} [(\frac{\sqrt 3}{2}) \cos 23 ° - (\frac{1}{2}) \sin 23 °]$
$= \frac{1}{2} [\cos 30 ° \cos 23 ° - \sin 30 ° \sin 23 °]$
Since, $c o s (A + B) = c o s A c o s B - s i n A s i n B$ ,
$= \frac{1}{2} [\cos (30 ° + 23 °)]$
$= \frac{1}{2} c o s (53 °)$
Hence, Option ‘D’ is Correct.

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14[√3cos23°-sin23°]=

The correct option is D NoneoftheseExplanation for the correct option:Given, 14√3cos23°-sin23°=12√3cos23°2-1.sin23°2=12√32cos23°–12sin23°=12cos30°cos23°−sin30°sin23°Since, cos(A+B)=cosAcosB–sinAsinB,=12[cos(30°+23°)]=12cos(53°)Hence, Option ‘D’ is Correct.

$\frac{1}{4} [\sqrt 3 \cos 23 ° - \sin 23 °] =$