Knowing that \(\displaystyle\alpha\) is acute and that

Lillianna Sandoval

Lillianna Sandoval

Answered question

2022-04-13

Knowing that α is acute and that sinαcosα=13, determine the exact value of
tan2αcot2α
I've used tanα=sinαcosα but can't seem to get anywhere. I get stuck here:
sinα+cosα3cos2αsin2α
when i use sin2α+cos2α=1 here it seems to get even more complicated.

Answer & Explanation

Kendall Wilkinson

Kendall Wilkinson

Beginner2022-04-14Added 17 answers

Squaring sinαcosα=13 , we get
sin2α2sinαcosα+cos2α=19
sinαcosα=49
which helps you with the denominator of your fraction.
We also get from this that
179=1+2sinαcosα
=sin2α+2sinαcosα+cos2α
=(sinα+cosα)2
Knowing that α is acute, you can take the square root here, and that should give you the numerator of your fraction.

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