Say yes or no.tan48∘tan23∘tan42∘tan67∘=1

LHS=tan48∘tan23∘tan42∘tan67∘ = tan48∘×tan23∘×tan(90∘− 48∘)×tan(90∘−23∘)= tan48∘×tan23∘×cot 48∘×cot 23∘= tan48∘×tan23∘×tan48∘1×tan23∘1=1∴LHS=RHS

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Say yes or no. 48^{}23^{}42^{}67^{} = 1

Question

Say yes or no.

$tan 4 8^{\circ} tan 2 3^{\circ} tan 4 2^{\circ} tan 6 7^{\circ} = 1$

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tan 4 8^{\circ} tan 2 3^{\circ} tan 4 2^{\circ} tan 6 7^{\circ} = 1

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L H S = tan 4 8^{\circ} tan 2 3^{\circ} tan 4 2^{\circ} tan 6 7^{\circ}

= tan 4 8^{\circ} \times tan 2 3^{\circ} \times tan (9 0^{\circ} - 4 8^{\circ}) \times tan (9 0^{\circ} - 2 3^{\circ})

= tan 4 8^{\circ} \times tan 2 3^{\circ} \times co t 4 8^{\circ} \times co t 2 3^{\circ}

= tan 4 8^{\circ} \times tan 2 3^{\circ} \times \frac{1}{tan 4 8 ^{\circ}} \times \frac{1}{tan 2 3 ^{\circ}} = 1

∴ L H S = R H S

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Question Text	Say yes or no. $tan 4 8^{\circ} tan 2 3^{\circ} tan 4 2^{\circ} tan 6 7^{\circ} = 1$
Answer Type	Text solution:1
Upvotes	150