Question

3xsin30+ytan^2 45=9 and ytan^2 60-xsec60=1 what is the value of x and y​

Answer 1

Answer:

$x = \frac{ - 35}{8 }$

And

$y = \frac{13}{4}$

Step-by-step explanation:

Given ,

$3x \sin30 \degree + y { \tan}^{2} 45 \degree = 9 \\ \\ \implies3x \times \frac{1}{2} + y \times {1}^{2} = 9 \\ \\ \implies \frac{3x}{2} + y = 9 \\ \\ \implies \: \frac{3x + 2y}{2} = 9 \\ \\ \implies3x + 2y = 18$

→ 2(3x + 2y ) = 2×18

→ 6x + 4y = 36 ---------> (1)

Again we have :

$y { \tan}^{2} 60 \degree - x \sec60 \degree = 1 \\ \\ \implies \: y ({ \sqrt{3}) }^{2} - x(2) = 1 \\ \\ \implies3y - 2x = 1$

→ 3(3y - 2x ) = 3

→ 9y - 6x = 3 -----------> (2)

Adding equation (1) and (2) we have

$6x + 4y + 9y - 6x = 36 + 3 \\ \\ \implies12y = 39 \\ \\ \implies \: y = \frac{39}{12} \\ \\ \implies \: y = \frac{13}{4}$

Now using the value of y in (2) :

$9( \frac{13}{4} ) + 6x = 3 \\ \\ \implies3( \frac{13}{4} ) + 2x = 1 \\ \\ \implies2x = 1 - \frac{39}{4} \\ \\ \implies2x = \frac{4 - 39}{4} \\ \\ \implies2x = \frac{ - 35}{4} \\ \\ \implies \: x = \frac{ - 35}{8}$