Answer to Question #167790 in Civil and Environmental Engineering for eyel

Question #167790

1.      Given that sin α =  and sin β = , find 𝑡𝑎𝑛 (α + β) if both α and β are in QIV.


1
Expert's answer
2021-03-04T06:02:51-0500


"\\sin \\alpha=a, -1\\leq a\\leq0"

"\\sin\\beta=b, -1\\leq a\\leq0"

"\\cos \\alpha=\\sqrt{1-\\sin^2 \\alpha}=\\sqrt{1-a^2}"

"\\cos\\beta =\\sqrt{1-\\sin^2 \\beta}=\\sqrt{1-b^2}"


"\\tan(\\alpha+\\beta)=\\dfrac{\\tan\\alpha+\\tan\\beta}{1-\\tan\\alpha\\tan\\beta}"

"=\\dfrac{\\dfrac{a}{\\sqrt{1-a^2}}+\\dfrac{b}{\\sqrt{1-b^2}}}{1-\\dfrac{a}{\\sqrt{1-a^2}}\\dfrac{b}{\\sqrt{1-b^2}}}"

"=\\dfrac{a\\sqrt{1-b^2}+b\\sqrt{1-a^2}}{\\sqrt{1-a^2}\\sqrt{1-b^2}-ab}"

"\\tan(\\alpha+\\beta)=\\dfrac{a\\sqrt{1-b^2}+b\\sqrt{1-a^2}}{\\sqrt{1-a^2}\\sqrt{1-b^2}-ab}"


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