horschler2571 horschler2571
  • 08-09-2020
  • Mathematics
contestada

prove that
tan² 20° + tan² 40° + tan² 80° = 33​

Respuesta :

hopemichael95
hopemichael95 hopemichael95
  • 09-09-2020

Answer:

Step-by-step explanation:

Now we know that

sec²θ -tan² θ= 1 ,

So tan²θ =sec²θ - 1

So the left of the given equation will be

sec²20 + sec²40 +sec²80 - 3

So

1/cos²20+1/cos²49+1/cos²80 -3

Remember sec θ= 1/cosθ

So

= since secθ = 1/cosθ

we have

= 1.1324 + 1.7040 + 33.1634 - 3

= 35.9998 - 3

= 33

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