Question

Show that tan 48°×tan 23°×tan 42°×tan 67°=1

Answer 1

Answer:Hence proved

Step-by-step explanation

Tan theta Is equal to cot 90 -theta

Tan48=cot42

Tan23=cot67

Substitute them in the question

Cot42*tan42*cot67*tan67

=1

Answer 2

$\huge\bold{Hey}$

$\textbf{Question - }$

Show that tan 48°×tan 23°×tan 42°×tan 67°=1

$\textbf{Solution - }$

tan 48°×tan 23°×tan 42°×tan 67°=1

—› tan48°×tan42°×tan67°×tan23°=1

—› tan48°×tan(90°–48°) ×tan67°×tan(90°–67°)=1

—› tan48°×cot48° × tan67°×cot67°=1

—› tan48°×1/tan48° × tan67°×1/tan67°=1

—› 1×1=1

—›1=1

LHS = RHS

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