The greatest integer less than or equal to cos290∘1+3sin250∘1 is

cos290∘1+3sin250∘1=cos(270o+20∘ ) 1+3sin(270o−20∘ ) 1=sin20∘ 1−3cos20∘ 1=3cos20∘ sin20∘ 3cos20∘ −sin20∘ =23 sin40∘ 2(23 cos20∘ −21sin20∘ ) =23 sin40∘ 2sin(60∘ −20∘ ) =3 4=2.31So, greatest integer value of given expression is 2

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The greatest integer less than or equal to {1}{ 290^{}}+{1}{{

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The greatest integer less than or equal to $\frac{1}{cos 29 0 ^{\circ}} + \frac{1}{3 sin 25 0 ^{\circ}}$ is

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\frac{1}{cos 29 0 ^{\circ}} + \frac{1}{3 sin 25 0 ^{\circ}}

= \frac{1}{cos ( 27 0 ^{o} + 2 0 ^{\circ} )} + \frac{1}{3 sin ( 27 0 ^{o} - 2 0 ^{\circ} )}

= \frac{1}{sin 2 0 ^{\circ}} - \frac{1}{3 cos 2 0 ^{\circ}}

= \frac{3 cos 2 0 ^{\circ} - sin 2 0 ^{\circ}}{3 cos 2 0 ^{\circ} sin 2 0 ^{\circ}}

= \frac{2 ( \frac{3}{2} cos 2 0 ^{\circ} - \frac{1}{2} sin 2 0 ^{\circ} )}{\frac{3}{2} sin 4 0 ^{\circ}}

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

= \frac{4}{3} = 2.31

So, greatest integer value of given expression is

2

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Question Text	The greatest integer less than or equal to $\frac{1}{cos 29 0 ^{\circ}} + \frac{1}{3 sin 25 0 ^{\circ}}$ is
Answer Type	Text solution:1
Upvotes	150

The greatest integer less than or equal to cos290∘1​+3​sin250∘1​ is

Text solutionVerified

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The greatest integer less than or equal to $\frac{1}{cos 29 0 ^{\circ}} + \frac{1}{3 sin 25 0 ^{\circ}}$ is