Question

if secA+tanA=3 then find cot A

Answer 1

Hey !!!

SecA + tanA = 3

1/cosA+sinA/cosA = 3

1 + sinA/cosA = 3

1 + sinA = 3cosA

(1 + sinA)² = (3cosA )² ⬅ Squaring in both side

1² + sin²A + 2sinA = 9cos²A

1² + sin²A + 2sinA = 9(1 - sin²A )

1 + sin²A + 2sinA + 9sin²A - 9 = 0

10sin²A + 2sinA - 8 = 0

2(5sin²A + sinA - 4 ) =0

5sin²A + sinA - 4 = 0 ➡Now it is in the form of quadratic equation like 5x² + x - 4 = 0

so, by using splitting method of quadratic equation .

5sinA² + 5sinA - 4sinA - 4 = 0 {splitting method }

5sinA(sinA + 1 ) - 4 ( sinA + 1) = 0

(5sinA - 4) ( sinA + 1) = 0

5sinA - 4 = 0

sinA = 4/5 and sinA + 1 = 0 sinA = -1 (neglect it )

now. sinA = 4/5 = p/h

b = √5² - 4² (PYTHAGORAS thoeorm)

b = √25-16

b = √9 = 3



cotA = b/p = 3/4Answer

***********************************

Hope it helps you !!

$\alpha$
Rajukumar111