Find the value of cos22∘2sin68∘−5tan75∘2cot15∘−53tan45∘tan20∘tan40∘tan50∘tan70∘.

⇒cos22∘2sin68∘−5tan75∘2cot15∘−53tan45∘tan20∘tan40∘tan50∘tan70∘=cos22∘2sin(90∘−22∘)−5tan75∘2cot(90∘−75∘)−53(1)(tan20∘tan70∘)(tan40∘tan50∘)=cos22∘2cos22∘−5tan75∘2tan75∘−53[tan(90∘−70∘)tan70∘][tan(90∘−50∘)tan50∘]=2−32−53(cot70∘tan70∘)(cot50∘tan50∘)[∴tan(90∘−θ)=cotθ,cot(90∘−θ)=tanθ&sin(90∘−θ)=cosθ]=2−52−53=2−1=1

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Find the value of {2 68^{}}{ 22^{}}-{2 15^{}}{5 75^{}}-{3 45^

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Find the value of $\frac{2 sin 6 8 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 cot 1 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 tan 4 5 ^{\circ} tan 2 0 ^{\circ} tan 4 0 ^{\circ} tan 5 0 ^{\circ} tan 7 0 ^{\circ}}{5}$ .

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\frac{2 sin 6 8 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 cot 1 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 tan 4 5 ^{\circ} tan 2 0 ^{\circ} tan 4 0 ^{\circ} tan 5 0 ^{\circ} tan 7 0 ^{\circ}}{5}

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\Rightarrow

\frac{2 sin 6 8 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 cot 1 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 tan 4 5 ^{\circ} tan 2 0 ^{\circ} tan 4 0 ^{\circ} tan 5 0 ^{\circ} tan 7 0 ^{\circ}}{5}

= \frac{2 sin ( 9 0 ^{\circ} - 2 2 ^{\circ} )}{cos 2 2 ^{\circ}} - \frac{2 cot ( 9 0 ^{\circ} - 7 5 ^{\circ} )}{5 tan 7 5 ^{\circ}} - \frac{3 ( 1 ) ( tan 2 0 ^{\circ} tan 7 0 ^{\circ} ) ( tan 4 0 ^{\circ} tan 5 0 ^{\circ} )}{5}

= \frac{2 cos 2 2 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 tan 7 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 [ tan ( 9 0 ^{\circ} - 7 0 ^{\circ} ) tan 7 0 ^{\circ} ] [ tan ( 9 0 ^{\circ} - 5 0 ^{\circ} ) tan 5 0 ^{\circ} ]}{5}

= 2 - \frac{2}{3} - \frac{3}{5} (cot 7 0^{\circ} tan 7 0^{\circ}) (cot 5 0^{\circ} tan 5 0^{\circ})

[∴ tan (9 0^{\circ} - θ) = cot θ, cot (9 0^{\circ} - θ) = tan θ & sin (9 0^{\circ} - θ) = cos θ]

= 2 - \frac{2}{5} - \frac{3}{5} = 2 - 1 = 1

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Question Text	Find the value of $\frac{2 sin 6 8 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 cot 1 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 tan 4 5 ^{\circ} tan 2 0 ^{\circ} tan 4 0 ^{\circ} tan 5 0 ^{\circ} tan 7 0 ^{\circ}}{5}$ .
Answer Type	Text solution:1
Upvotes	150

Find the value of cos22∘2sin68∘​−5tan75∘2cot15∘​−53tan45∘tan20∘tan40∘tan50∘tan70∘​.

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Find the value of $\frac{2 sin 6 8 ^{\circ}}{cos 2 2 ^{\circ}} - \frac{2 cot 1 5 ^{\circ}}{5 tan 7 5 ^{\circ}} - \frac{3 tan 4 5 ^{\circ} tan 2 0 ^{\circ} tan 4 0 ^{\circ} tan 5 0 ^{\circ} tan 7 0 ^{\circ}}{5}$ .