Question

tan 48°tan 23° tan 42° tan 67° tan 45º = 1​

Answer 1

Using the formula cot(90-θ) = tan θ

tan (48) = cot (90-48) = cot 42

tan (23) = cot (90-23) = cot 67

Also ,we know that tan θ x cot θ = 1.

So, the given equation is :-

tan 48 x tan 23 x tan 42 x tan 67 x tan 45

= cot 42 x cot 67 x tan 42 x tan 67 x tan 45.

tan 45 = 1

= (cot 42 x tan 42) x (cot 67 x tan 67) x 1

= 1 x 1 x 1 = 1

Hence Proved LHS=RHS