sin 1 2 ∘ sin 4 8 ∘ sin 5 4 ∘ = a 1 then the value of a is

Let θ = 1 2 ∘ . L.H.S. = s i n 7 2 ∘ 1 sin 1 2 ∘ sin 4 8 ∘ sin 7 2 ∘ sin 5 4 ∘ = 4 1 ⋅ s i n 7 2 ∘ s i n 3 ( 1 2 ∘ ) sin 5 4 ∘ = 4 s i n 7 2 ∘ s i n 3 6 ∘ s i n 5 4 ∘ = 8 s i n 3 6 ∘ c o s 3 6 ∘ s i n 3 6 ∘ c o s 3 6 ∘ = 8 1 . Hence a = 8 .

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minQB

MathematicsMediuminteger

$sin 1 2^{\circ} sin 4 8^{\circ} sin 5 4^{\circ} = \frac{1}{a}$ then the value of $a$ is

Answer:

Solution:

Let $θ = 1 2^{\circ}$ . L.H.S. $= \frac{1}{s i n 7 2 ^{\circ}} sin 1 2^{\circ} sin 4 8^{\circ} sin 7 2^{\circ} sin 5 4^{\circ} = \frac{1}{4} \cdot \frac{s i n 3 ( 1 2 ^{\circ} )}{s i n 7 2 ^{\circ}} sin 5 4^{\circ} = \frac{s i n 3 6 ^{\circ} s i n 5 4 ^{\circ}}{4 s i n 7 2 ^{\circ}} = \frac{s i n 3 6 ^{\circ} c o s 3 6 ^{\circ}}{8 s i n 3 6 ^{\circ} c o s 3 6 ^{\circ}} = \frac{1}{8}$ . Hence $a = 8$ .

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: QB

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