Question

please solve the problem. wrong answer will be reported ​

Answer 1

$11. \red{ Cos 43 \degree = \frac{x}{\sqrt{x^{2} + y^{2}} }}$

$\implies sec 43 \degree = \frac{\sqrt{x^{2} + y^{2}}}{x}$

$\implies sec( 90 - 47 ) = \frac{\sqrt{x^{2} + y^{2}}}{x}$

$\implies Cosec 47 \degree = \frac{\sqrt{x^{2} + y^{2}}}{x} \: --(2)$

$cot ^{2} 47 \degree\\ = cosec^{2} 47 \degree - 1 \\= \Big(\frac{\sqrt{x^{2} + y^{2}}}{x}\Big)^{2} - 1 \\= \frac{x^{2} + y^{2}}{x^{2} } - 1 \\= \frac{x^{2} + y^{2} - x^{2} }{x^{2}} \\= \frac{y^{2}}{x^{2}}$

$\implies cot 47\degree = \frac{y}{x}$

$\implies tan 47\degree = \frac{x}{y}$

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