Question

find the value of tan² 30° + tan²45 ° + tan²60 °​

Answer 1

Answer:

13/3.

General results :-)

$tan 30° = \frac{1}{\sqrt{3}} \\ \\ tan 45° = 1 \\ \\ tan 60°=\sqrt{3}$

Using above values we can easily find the value of given expression as shown below :-)

tan² 30° + tan²45 ° + tan²60°

$= (\sqrt{ { \frac{1}{3} }} ) {}^{2} + ( {1)}^{2} + ( { \sqrt{3} })^{2} \\ \\ = \frac{1}{3} + 1 + 3 \\ \\ = \frac{1 + 3 + 9}{3} \\ \\ = \frac{13}{3}$

So,

the value of given expression in the question is 13/3 .

Answer 2

Answer:

tan^2(30)+tan^2(45)+tan^2(60)

= tan^2(30)+tan^2(45)+cot^2(30)

=1+1

=2

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