WAEC 2019 · Paper 2 · Q4

(a)
If $\cos\theta = \frac{15}{17}$ , find the value of $\dfrac{\tan\theta}{1 + 2\tan\theta}$ .
(b)
Find the value of $y$ if $\dfrac{\log_{10} y}{\log_{10} 64} = \frac12$ .

Worked solution (try it first)

(a)

$\cos\theta = \frac{15}{17}$ : the opposite side is $\sqrt{17^2 - 15^2} = \sqrt{64} = 8$ , so $\tan\theta = \frac{8}{15}$ .
Then $\frac{\tan\theta}{1 + 2\tan\theta} = \frac{\frac{8}{15}}{\frac{31}{15}}$
$= \frac{8}{31}$ .

(b)

Multiply both sides by $\log_{10} 64$ : $\log_{10} y = \frac12\log_{10} 64$
$= \log_{10} 64^{\frac12}$
$= \log_{10} 8$ .
So $y = 8$ .

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