Question

show that tan48° tan16° tan42° tan45° tan74°=1​

Answer 1

Step-by-step explanation:

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Answer 2

To prove-

tan48° tan16° tan42° tan45° tan74°=1

Solution-

LHS

tan48° tan16° tan42° tan45° tan74°

using formula:

tan∆ = cot(90-∆)

tan48°× tan16°× tan(90°-48°)× tan45°× tan(90°-16°)

tan48°×tan16°×cot48°×tan45°×cot16°

using formula

tan∆= 1/cot∆

tan48°×tan16°×1/tan48°×tan45°×1/tan16°

cancelling we get

tan45°

=1 =RHS

LHS=RHS