Question 89 of 155MediumMCQ
If α=cos−153, β=tan−131, where 0<α,β<2π, then α−β is equal to: Solutions · 1
Official solution
cosα=53⇒tanα=34. Also tanβ=31.
\[\tan(\alpha-\beta)=\frac{\frac43-\frac13}{1+\frac43\cdot\frac13}=\frac{1}{\frac{13}{9}}=\frac{9}{13}.\]
With opposite =9, adjacent =13, hypotenuse =81+169=250=510:
\[\alpha-\beta=\tan^{-1}\frac{9}{13}=\sin^{-1}\frac{9}{5\sqrt{10}}.\] Answer the question to unlock