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tan60*tan42*tan66*tan78=? the angles are in degrees.

tan60*tan42*tan66*tan78=?


the angles are in degrees.

Grade:11

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Aritra,

 

Here we use, tanxtan(60-x)tan(60+x) = tan3x -------{a standard formula}.

so consider tan18tan42tan78 = tan18tan(60-18)tan(60+18) = tan54.

So tan42tan78 = tan54/tan18-------(1)

 

Now consider tan6tan54tan66 = tan18.

So tan6tan66 = tan18/tan54-------(2)

 

Hence tan6tan42tan66tan78 = tan54/tan18 * tan18/tan54 = 1.

 

Note the first term is tan6, not tan60.

 

Hence value is 1.

 

Hope that helps.

All the best.

Regards,

Ashwin (IIT Madras).

niteesh kumar
12 Points
6 years ago
tan60tan660tan420tan780=1

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