Use the following conditions to find the exact value of \tan(\alpha-\beta)

EunoR

EunoR

Answered question

2021-08-13

Use the following conditions to find the exact value of tan(αβ)
sinα=45,π2<α<π
cosβ=513,0<β<π2

Answer & Explanation

smallq9

smallq9

Skilled2021-08-14Added 106 answers

Trigonometry:
sinα=45,π2<α<π
cosβ=513,0<β<π2
We need to find tan(αβ)=tanαtanβ1+tanαtanβ
For α, base =5242=3
for β, perpendicular =13252=12
Therefore tanα=43
tanβ=125
Therefore tan(αβ)=tanαtanβ1+tanαtanβ
=431251+(43)(125)
=56153315
=5633

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