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Question Number 89662 by 974342176 last updated on 18/Apr/20

$$Giventhat\sin A=\frac{1}{2}and\sin C=\frac{\sqrt{3}}{2}withoutu$$$$usingcalculatorsolve$$$$a)\tan (A+C)$$$$b)cos(A-C)$$

Answered by TANMAY PANACEA. last updated on 18/Apr/20

$$sinA=\frac{1}{2}=sin{30}^o\to A={30}^o$$$$sinC=\frac{\sqrt{3}}{2}=sin{60}^o\to C={60}^o$$$$tan(A+C)=tan\left({90}^o\right)=\mathrm{\infty }$$$$cos(A-C)=cos(-{30}^o)=cos\left({30}^o\right)=\frac{\sqrt{3}}{2}$$$$$$

Commented by jagoll last updated on 19/Apr/20

$$\mathrm{how}\mathrm{about}\mathrm{C}={120}^{\mathrm{o}}$$$$\mathrm{then}\tan (\mathrm{A}+\mathrm{C})=\tan {150}^{\mathrm{o}}$$$$=-\tan {30}^{\mathrm{o}}=-\frac{1}{\sqrt{3}}$$

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