Answer to Question #283603 in Trigonometry for Yiom Pangol

Question #283603

Show that d= 2v² costheta sintheta(0_x)/gcos²thetax


1
Expert's answer
2021-12-30T17:24:42-0500

Since the question is unclear, we assume as follows:

Show that "\\dfrac{\\cos \\theta-\\sin \\theta}{\\cos \\theta+\\sin \\theta}=\\sec 2 \\theta-\\tan 2 \\theta" .

Solution:

"\\dfrac{\\cos \\theta-\\sin \\theta}{\\cos \\theta+\\sin \\theta}"

multiplying and dividing by \cos \theta-\sin \theta

"=\\frac{\\cos \\theta-\\sin \\theta}{\\cos \\theta+\\sin \\theta} \\times \\frac{\\cos \\theta-\\sin \\theta}{\\cos \\theta-\\sin \\theta}"

simplifying and using trigonometric identities

"\\begin{aligned}\n\n&=\\frac{(\\cos \\theta-\\sin \\theta)^{2}}{\\cos ^{2} \\theta-\\sin ^{2} \\theta}=\\frac{\\cos ^{2} \\theta+\\sin ^{2} \\theta-2 \\sin \\theta \\cos \\theta}{\\cos 2 \\theta} \\\\\n\n&=\\frac{1-\\sin 2 \\theta}{\\cos 2 \\theta}=\\sec 2 \\theta-\\tan 2 \\theta\n\n\\end{aligned}"


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