Fewpal
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solve: tan6. tan42.tan66. tan78

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Solution:

Method 1 -

Use Trigonometric Identity 

tanx * tan(60 - x) * tan(60 + x) = tan(3x) 

set x = 6 

tan6 * tan54 * tan66 = tan18 .................... ((1)) 

Similarly, set x = 18 

tan18 * tan42 * tan78 = tan54 ...................... ((2)) 

((1)) * ((2)): 

tan6 * tan54 * tan66 * tan18 * tan42 * tan78 = tan18 * tan54 

tan6 * tan66 * tan42 * tan78 = 1 

 

Method 2 -

Given - tan 6 tan 42 tan 66  tan 78 

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