Question #167790

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

Expert's answer

"\\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}"

"=\\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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