Question

show that tan 48 degree tan 23 degree tan 42 degree tan 67 degree is equal to 1

Answer 1

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Answer 2

$Value \:of \: tan 48 \degree tan 23 \degree tan 42 \degree tan 67 \degree$

/* Rearranging the terms, we get */

$= (tan 48 \degree tan 42 \degree)\times( tan 23 \degree tan 67 \degree )$

$= [tan 48 \degree tan (90 - 48) \degree)\times( tan 23 \degree tan (90-23) \degree )$

$= (tan 48 \degree cot 48 \degree)\times( tan 23 \degree cot 23 \degree )$

$= 1 \times 1$

$\boxed { \pink {Since, tan \theta \times cot \theta = 1 }}$

$= 1$

Therefore.,

$\red{Value \:of \: tan 48 \degree tan 23 \degree tan 42 \degree tan 67 \degree}\green {=1}$

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