Find the value of the following :−(logsin260∘sec230∘)

sin260∘=(23)2=43 and sec230∘=(32)2=34∴logsin260∘sec230∘=log3/4(34)=log3/4(43)−1=−1.log(3/4)(43)=−1Hence, −(logsin260∘sec230∘)=1

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Find the value of the following : -( _{^{2}60^{}}^2 30^{})

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Find the value of the following :
$- (lo g_{s i n^{2} 6 0^{\circ}} sec^{2} 3 0^{\circ})$

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Liam Discussed

Find the value of the following :

- (lo g_{s i n^{2} 6 0^{\circ}} sec^{2} 3 0^{\circ})

9 mins ago

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9 mins ago

sin^{2} 6 0^{\circ} = (\frac{3}{2})^{2} = \frac{3}{4}

and

sec^{2} 3 0^{\circ} = (\frac{2}{3})^{2} = \frac{4}{3}

∴ lo g_{s i n^{2} 6 0^{\circ}} sec^{2} 3 0^{\circ} = lo g_{3/4} (\frac{4}{3})

= lo g_{3/4} (\frac{3}{4})^{- 1} = - 1. lo g_{(3/4)} (\frac{3}{4}) = - 1

Hence,

- (lo g_{s i n^{2} 6 0^{\circ}} sec^{2} 3 0^{\circ}) = 1

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Question Text	Find the value of the following : $- (lo g_{s i n^{2} 6 0^{\circ}} sec^{2} 3 0^{\circ})$
Answer Type	Text solution:1
Upvotes	150