Question

Marks: 3
Q.No.:34
Prove that
tan 48°tan 23°tan 42°tan 67°tan 45º = 1
​

Answer 1

Answer:

Proven that it is 1.

Step-by-step explanation:

tan 48 tan 23 tan 42 tan 67 tan 45 = 1

=> (tan 48 tan 42)(tan 23 tan 67) tan 45 = 1

now, tan 45 = 1 as we know,

=> (tan 48 tan 42)(tan 23 tan 67) = 1

=> (tan 48/cot 42)(tan 23/cot 67) = 1    (since tan A = 1/cot A)

=> [tan 48/cot (90 - 48)][(tan 23/cot (90 - 23)] = 1 (since they're complements)

=> (tan 48/tan 48)(tan 23/tan 23) = 1 (since cot(90 - A) = tan A)

=> 1/1 = 1

therefore, LHS = RHS. Hence proved.