Question

show that - : tan 20° tan 40° tan 80° = tan 60°​

Answer 1

Answer:

⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

tan 40 * tan 80* tan 20=(sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20

now, multiplying numerator and denominator by 2,

=(2*sin 40*sin 80) *sin 20 /(2 cos 40*cos 80) cos 20]

=(cos 40- cos 120)*sin 20/( (cos 120+ cos 40) cos 20

=(2 cos 40 +1) sin 20 /(2 cos 40-1) cos 20

=(2 cos 40*sin 20 +sin 20) /(2 cos 40 cos 20 -cos 20)

=(sin 60 -sin 20 +sin 20)/ (cos 60+sin 20-sin 20)

= sin 60/cos 60

=tan 60

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Step-by-step explanation:

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Answer 2

Answer:

tan20.tan40.tan60

we can write a

cot(90-20).cot(90-40).tan60

cot70.cot60.tan60

cot(45+30).cot60.tan60

formula

{(cot45.cot30 - 1/cot 45 + cot 30 = cot (45+30)}

now

cot45.cot30 - 1/cot 45 + cot 30 .cot60.tan60

put values

1.√3-1/1+√3×1

√3-1/1+√3

2/1+3+ 2√3

tan60

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