Question

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

Answer 1

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