Question

show that tan48°.tan23°tan42°.42°.tan67°=1

Answer 1

question is not correct plz check it again

Answer 2

Here we need to prove

tan 48° . tan 23° . tan 42° . tan 67 = 1

In such questions we need to see complimentary angles (whose sum is 90)

and we change one of them into complimentary of other  trigonometric ratio ( sin Ф to cos Ф, tan Ф to cot Ф, sec Ф to cosec Ф) so that we can eliminate them or can use any trigonometric identity.

LHS

tan 48° . tan 23° . tan 42° . tan 67

Which can be written as

tan (90 - 42)° . tan (90 - 67)° . tan 42° . tan 67°

cot 42° . cot 67° . tan 42°. tan 67° [∵ tan (90 - Ф) = cot Ф]

Also, cot Ф = 1 / tan Ф

$\frac{1}{tan 42} \times  \frac{1}{tan 67} \times tan 42 \times tan 67$

= 1 = RHS, Hence Proved