Math, asked by rimidutta, 10 months ago

Show that
tan48× tan23× tan67= 1

Answers

Answered by nix38

=tan48×tan(90-67)×tan67

=tan48×cot67×tan67

=tan48

that's the answer man

rimidutta: but you have to prove that the answer is one but you show the different method

shadowsabers03: Hey, I think your question is incomplete and it needs some values too.

I think the question includes tan 42 too!!!

shadowsabers03: Please check it and reply me.

hipsterizedoll410: Yes u r right @sanjeev

shadowsabers03: That's it!

Answered by hipsterizedoll410

I think there must be tan42° so the product will be 1.

tan48°×tan23°×tan42°×tan67° = 1

Solving LHS,

We know that 48+42 = 90

hence, 42 = 90-48

and 67+23 = 90

67 = 90-23

Now, substitutes those value but now there will be a cot sign, so

tan 48°×cot 48°×tan 23°× cot 23°

Here tan and cot will be cancel out so,

1×1

Hence proved.

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