Answer to Question #146976 in Trigonometry for Hazel

Question #146976
Sin(y)+sin(y)cot^2(y)=cosec(y)
1
Expert's answer
2020-12-02T01:52:05-0500

Explanations & Calculations


  • Start the proof with the Left hand side as there are more terms present

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\sin y +\\sin y \\cot^2 y &=\\small\\sin y (1+\\cot^2 y)\\\\\n&=\\small \\sin y\\Big(1+\\frac{\\cos^2 y}{\\sin^2 y}\\Big)\\\\\n&= \\small \\sin y \\Big(\\frac{\\sin^2 y+\\cos^2 y}{\\sin^2 y}\\Big)\\\\\n&=\\small \\sin y\\times \\frac{1}{\\sin^2 y}\\\\\n&=\\small\\frac{1}{\\sin y}\\\\\n&= \\small \\cosec y\\\\\n\\end{aligned}"


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