Question

Evaluate each of the following tan² 30° + tan² 45° + tan² 60°

Answer 1

SOLUTION:

Given :  

tan² 30° + tan² 45° + tan² 60°                                              

= (1/√3)² + (√3)² + 1

= ⅓ + 3 + 1

[√3 × √3 = 3]

= ⅓ + 4

= ⅓ + 4/1

= (1 + 4×3) /3

[ By taking L.C.M]

= (1 + 12)/3 = 13/3

tan² 30° + tan² 45° + tan² 60° = 13/3

[tan 30° = 1/√3,  tan 60° = √3, tan 45° = 1]

Hence, tan² 30° + tan² 45° + tan² 60° = 13/3

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :-


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To evaluate of : tan² 30° + tan² 45° + tan² 60°


Salutation :

tan² 30° + tan² 45° + tan² 60°

= ( 1 / √3 )² + ( 1 )² + ( √3 )²

= 1 / 3 + 1 + 3

= ( 1 + 3 + 9 ) / 3

= 13 / 3


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Since ,

tan30° = 1 / √3

tan45° = 1

tan60° = √3

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