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Prove That: Sin 18 ∘ Cos 72 ∘ + √ 3 ( Tan 10 ∘ Tan 30 ∘ Tan 40 ∘ Tan 50 ∘ Tan 80 ∘ ) - Mathematics

Sum

Prove that:

`sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ  tan50^circ tan 80^circ) `

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Solution

`"LHS" =  sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ  tan50^circ tan 80^circ) `

`=(sin 18^circ)/sin(90^circ -72^circ) + sqrt(3)   [cot(90^circ - 10^circ)xx1/sqrt(3)xxcot(90^circ - 40^circ )xxtan50^circ]` 

`=(sin 18^circ)/(sin 18^circ) + sqrt(3) (cot 80^circxxcot 50^circ)xxtan 50^circxxtan 80^circ)/)`

`= 1 + (1/tan 80^circxx1/ tan 50^circxxtan 50^circxxtan 80^circ)`

= 2

= RHS

Concept: Trigonometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercise | Q 4.4 | Page 313
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