If sin theta 12 13 find the value of sin

Asked by admin @ 04/08/2021 in Math viewed by 359 People

if sin theta = 12/13 find the value of sin^2 theta - cos^2 theta /2 sin theta.cos theta * 1/tan^2 theta

Answered by admin @ 04/08/2021

Answer:

$Value \: of \\\frac{(sin^{2}\theta-cos^{2}\theta)}{2sin\theta cos\theta}\times \frac{1}{tan^{2}\theta}\\=\frac{595}{3456}$

Step-by-step explanation:

$Given ,\\sin\theta = \frac{12}{13}--(1)$

$cos^{2}\theta = 1-sin^{2}\theta \\=1-\left(\frac{12}{13}\right)^{2}\\=1-\frac{144}{169}\\=\frac{169-144}{169}\\=\frac{25}{169}$

$cos\theta = \sqrt{\frac{25}{169}}\\=\frac{5}{13}--(2)$

$tan\theta = \frac{sin\theta}{cos\theta}\\=\frac{\frac{12}{13}}{\frac{5}{13}}\\=\frac{12}{5}--(3)$

$Now,Value \: of \\\frac{(sin^{2}\theta-cos^{2}\theta)}{2sin\theta cos\theta}\times \frac{1}{tan^{2}\theta}$

$=\frac{sin^{2}\theta-(1-sin^{2}\theta)}{2sin\theta cos\theta }\times \frac{1}{tan^{2}\theta}$

$=\frac{(2sin^{2}\theta-1)}{2sin\theta cos\theta}\times \frac{1}{tan^{2}\theta}$

$=\frac{[2\big(\frac{12}{13}\big)^{2}-1]}{2\times \frac{12}{13}}\times \frac{5}{13}\times \frac{1}{\big(\frac{12}{5}\big)^{2}}$

$=\frac{2\times \frac{144}{169}-1}{2\times \frac{12}{13}\times \frac{5}{13}}\times \frac{25}{144}$

$=\frac{\frac{(288-169)}{169}}{\frac{120}{169}}\times \frac{25}{144}$

$=\frac{119\times 5}{24 \times 144}=\frac{ 595}{3456}$

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If sin theta 12 13 find the value of sin

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