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Question Number 206425 by hardmath last updated on 13/Apr/24

$$\mathrm{If}\cos \mathit{\alpha }=\frac{3}{5}(0<\mathit{\alpha }<\frac{\mathit{\pi }}{2})$$$$\mathrm{Find}:\frac{{\tan }^2(45°+\frac{\mathit{\alpha }}{2})}{3}=?$$

Answered by MM42 last updated on 13/Apr/24

$${tan}^{2}a=\frac{1-cos2a}{1+cos2a}$$$$\Rightarrow {tan}^2(45+\frac{a}{2})=\frac{1-cos(90+a)}{1+cos(90+a)}$$$$=\frac{1+sina}{1-sina}=\frac{1+\frac{4}{5}}{1-\frac{4}{5}}=9\Rightarrow ans=3✓$$$$$$

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