Question

prove that tan 38° . tan 50° .tan 40° . tan 52° = 1​

Answer 1

Answer:

tan(x)=cot(90-x) and tan(x)*cot(x)=1

Step-by-step explanation:

Here the above can be written as

LHS

tan38.tan52.tan50.tan40

= tan38*cot(90-52).tan50*cot(90-40)

=tan38.cot38.tan50.cot50

=1*1

=1

LH=RHS

Hence proved

Answer 2

Step-by-step explanation:

we take in the order like tan 38 . tan 52 . tan 50 . tan 40

the complementary angle of tan like this:

we can write tan ( 90- 52) in the place of in tan 38

similarly

tan( 90 - 52) . tan 52 . tan ( 90- 40) . tan 40

cot 52 . tan 52 . cot 40 . tan 40

1/ tan 52 . tan 52 . 1/ tan40 . tan 40

tan 52 tan 52 gets cancel an tan 40 tan 40 gets cancel

so the remaining is one