If -30- and -60- then the value of sin- 2 -tan-15-tan-2-15-tan- is

The correct option is A 726(4√(3) 3)sinα+2α+tan(α+15^∘)tanβ+(β2+15^∘)+tanα =sin30^∘+60^∘+tan45^∘tan60^∘+45^∘+tan30^∘ =12+2+1√(3)+1+1√(3) =7√(3)2(4+√(3))=726 ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Common Angles

If α=30∘ and ...

Question

If $α = 30^{\circ}$ and $β = 60^{\circ}$ , then the value of $\frac{sin α + sec 2 α + tan (α + 15^{\circ})}{tan β + cot (\frac{β}{2} + 15^{\circ}) + tan α}$ is

\frac{7}{26} (4 \sqrt{3} - 3)

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3 (4 - \sqrt{3})

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\frac{1}{2} (\sqrt{3} - 1)

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\sqrt{3} - 2

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Solution

The correct option is A $\frac{7}{26} (4 \sqrt{3} - 3)$
$\frac{sin α + sec 2 α + tan (α + 15^{\circ})}{tan β + cot (\frac{β}{2} + 15^{\circ}) + tan α}$

$= \frac{sin 30^{\circ} + sec 60^{\circ} + tan 45^{\circ}}{tan 60^{\circ} + cot 45^{\circ} + tan 30^{\circ}}$

$= \frac{\frac{1}{2} + 2 + 1}{\sqrt{3} + 1 + \frac{1}{\sqrt{3}}}$

$= \frac{7 \sqrt{3}}{2 (4 + \sqrt{3})} = \frac{7}{26} (4 \sqrt{3} - 3)$

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If α=30∘ and β=60∘, then the value of sinα+sec2α+tan(α+15∘)tanβ+cot(β2+15∘)+tanα is

The correct option is A 726(4√3−3)sinα+sec2α+tan(α+15∘)tanβ+cot(β2+15∘)+tanα =sin30∘+sec60∘+tan45∘tan60∘+cot45∘+tan30∘ =12+2+1√3+1+1√3 =7√32(4+√3)=726(4√3−3)

If $α = 30^{\circ}$ and $β = 60^{\circ}$ , then the value of $\frac{sin α + sec 2 α + tan (α + 15^{\circ})}{tan β + cot (\frac{β}{2} + 15^{\circ}) + tan α}$ is