Question

show that tan 48 ° tan 23° tan 42° tan 67°=1​

Answer 1

Answer:

tan 48.tan42 = tan 90 = 1

tan23.tan67 = tan90 = 1

so tan 90.tan90 = 1

which is equal to RHS

PROVED.

Step-by-step explanation:

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Answer 2

Given:

• tan 48° tan 23° tan 42° tan 67° = 1

Solution

We can also write tan functions in terms of cot functions,

$\\ \colon\implies{\tt{ tan \ 48° = tan \ (90° – 42°) = cot \ 42° }} \\ \\ \\ \colon\implies{\tt{tan \ 23° = tan \ (90° – 67°) = cot \ 67° }}$

Hence,

Substituting these values,

$\\ \colon\implies{\tt{ cot \ 42° \ cot \ 67° \ tan \ 42° \ tan \ 67° }} \\ \\ \\ \colon\implies{\tt{ (cot \ 42° tan \ 42°) (cot \ 67° \ tan 67°) }} \\ \\ \\ \colon\implies{\tt{ 1 \times 1 }} \: \: \: \: \: {\sf\red{[Since \ cot \ A.tan \ A = 1]}} \\ \\ \\ \colon\implies{\boxed{\tt\gray{ 1 }}}$

Hence Proved ..!