Question

12cosx+5sinx=13 value of tanx

Answer 1

I hope it will help u

Answer 2

The value of tanx is 5/12.

• We know that sin²x + cos²x =1
• Now dividing both sides by cos²x, we get

tan²x + 1 = $\frac{1}{cos^2x}$    (Equation 1)

• Now the given equation is 12cosx+5sinx =13

• Dividing both sides by cosx we get,

12 + 5 tanx = $\frac{13}{cosx}$

• Squaring both sides, we get

144 + 120 tanx + 25tan²x = $\frac{169}{cos^2x}$    

144 + 120 tanx + 25tan²x = 169(1+tan²x)          (From equation 1)

144 + 120 tanx + 25tan²x = 169+169tan²x

144tan²x - 120 tanx + 25 = 0

(12tanx)² - 2×12tanx×5 + 5² =0

(12tanx-5)²=0

12tanx-5=0

tanx = 5/12

• The value of tanx is 5/12.