Without using trigonometric tables, evaluate the following:2(sin32∘cos58∘)−3(tan15∘tan60∘tan75∘cos38∘cosec 52∘).

Let I=2(sin320cos580 )−3(tan150tan600tan750cos380cosec 520 )We have tan(90−θ)=cotθ and cos(90−θ)=sinθ=2(sin320cos(90−32) )−3(tan150tan600tan(90−15)cos(90−52)cosec 520 )=2(sin320sin320 )−3(tan150×3×cot150sin520cosec 520 )We have sinθ×cosecθ=1 and tanθ×cotθ=1Using this we evaluate the above expression as I=2−3(3 1 )=2−1=1

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Without using trigonometric tables, evaluate the following: 2

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Without using trigonometric tables, evaluate the following:
$2 (\frac{cos 5 8 ^{\circ}}{sin 3 2 ^{\circ}}) - 3 (\frac{cos 3 8 ^{\circ} cosec 5 2 ^{\circ}}{tan 1 5 ^{\circ} tan 6 0 ^{\circ} tan 7 5 ^{\circ}})$ .

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Without using trigonometric tables, evaluate the following:

2 (\frac{cos 5 8 ^{\circ}}{sin 3 2 ^{\circ}}) - 3 (\frac{cos 3 8 ^{\circ} cosec 5 2 ^{\circ}}{tan 1 5 ^{\circ} tan 6 0 ^{\circ} tan 7 5 ^{\circ}})

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Text solutionVerified

Let

I = 2 (\frac{cos 58 ^{0}}{sin 32 ^{0}}) - 3 (\frac{cos 38 ^{0} cosec 52 ^{0}}{tan 15 ^{0} tan 60 ^{0} tan 75 ^{0}})

We have

tan (90 - θ) = cot θ

and

cos (90 - θ) = sin θ

= 2 (\frac{cos ( 90 - 32 )}{sin 32 ^{0}}) - 3 (\frac{cos ( 90 - 52 ) cosec 52 ^{0}}{tan 15 ^{0} tan 60 ^{0} tan ( 90 - 15 )})

= 2 (\frac{sin 32 ^{0}}{sin 32 ^{0}}) - 3 (\frac{sin 52 ^{0} cosec 52 ^{0}}{tan 15 ^{0} \times 3 \times co t 15 ^{0}})

We have

sin θ \times cosec θ = 1

and

tan θ \times co tθ = 1

Using this we evaluate the above expression as

I = 2 - 3 (\frac{1}{3}) = 2 - 1 = 1

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Question Text	Without using trigonometric tables, evaluate the following: $2 (\frac{cos 5 8 ^{\circ}}{sin 3 2 ^{\circ}}) - 3 (\frac{cos 3 8 ^{\circ} cosec 5 2 ^{\circ}}{tan 1 5 ^{\circ} tan 6 0 ^{\circ} tan 7 5 ^{\circ}})$ .
Answer Type	Text solution:1
Upvotes	150

Without using trigonometric tables, evaluate the following:2(sin32∘cos58∘​)−3​(tan15∘tan60∘tan75∘cos38∘cosec 52∘​).

Text solutionVerified

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Without using trigonometric tables, evaluate the following:
$2 (\frac{cos 5 8 ^{\circ}}{sin 3 2 ^{\circ}}) - 3 (\frac{cos 3 8 ^{\circ} cosec 5 2 ^{\circ}}{tan 1 5 ^{\circ} tan 6 0 ^{\circ} tan 7 5 ^{\circ}})$ .