Question

Tan 48°. tan 16º. tan 42° .tan 74°
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Answer 1

Step-by-step explanation:

tan 48° × tan 16° × tan 42° × tan 74°

= tan(90°-42°)×tan42°×tan(90°-74°)×tan74°

= cot 42° × tan 42° × cot 74° × tan 74°

= 1×1 = 1 ( cot∅ × tan∅ = 1 )

Answer 2

• Tan 48⁰ tan 74⁰ tan 42⁰ tan 16⁰ = 1

Rearrange the terms for easy processing

• Tan 48⁰ tan 42⁰ tan 74⁰ tan 16⁰ = 1

• Tan ( 90⁰ - 42⁰) tan 42⁰ tan ( 90⁰ - 16⁰) tan 16⁰ = 1

Tan cot 42⁰ tan 42⁰ cot 16⁰ tan 16⁰ = 1

$\frac{1}{ \tan(42 {}^{0} ) } \times \tan(22 {}^{0} ) \times \frac{1}{ \tan(16 {}^{0} ) } \times \tan(16 {}^{0} ) = 1$

LHS = RHS