Math, asked by tummakeerthana19, 2 months ago

if cosecø+cotø=1/3, find cosø and determine the quadrant in which ø lies​

Answers

Answered by nehaliganvit3
0

Step-by-step explanation:

2x-1/3=1/5-6

6x-3/3=1-5x/5

30x-5=3-15x

45x=8

x=8/45

Answered by ravi2303kumar
1

Step-by-step explanation:

cosecø+cotø=1/3

=> (cosecø+cotø)²=(1/3)²

=> cosec²ø + cot²ø = (1/9)+2cosecø.cotø  ---------- (1)

(cosecø+cotø)/cosecø-cotø  * (cosecø-cotø)

1/(cosecø-cotø) = 1/3

=> (cosecø-cotø) = 3

=>(cosecø-cotø)² = 3²

=> cosec²ø + cot²ø = 9-2cosecø.cotø  -------------- (2)

by (1) and (2),

=> (1/9)+2cosecø.cotø = 9-2cosecø.cotø

4cosecø.cotø = 9-(1/9)

4cosecø.cotø = 80/9

cosecø.cotø = 20/9

9cosø = 20sin²ø

9cosø = 20(1-cos²ø)

20cos²ø+9cosø-20 = 0

let cosø=x

=> 20x²+9x-20 = 0

=> 20x²+25x - 16x -20 = 0

=> 20x²- 16x+25x  -20 = 0

=> 4x(5x-4) + 5(5x-4) = 0

=> (5x-4)(4x+5) = 0

=>  x = 4/5   or x= -5/4

when x = 4/5

ie.,  when cosø = 4/5

=> 0 < cosø < 1

=>  90° < ø < 0°

=> ø will not lie in the First quadrant

when x = -5/4

ie.,  when cosø = -5/4

=> 0 > cosø <  -1

=>  90° > ø < 180°

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