Question

If 3 cot( theta)= 1 ,then find the value of
$3 cos( theta) - 4sin(theta)\div 5sin(theta) + 4cos(theta)$
​

Answer 1

Step-by-step explanation:

value of

3 cos( theta) - 4sin(theta)\div 5sin(theta) + 4cos(theta)3cos(theta)−4sin(theta)÷5sin(theta)+4cos(theta)

Given:-

3cotθ= 1

cotθ= 1 = b

3. p

.:b= 1 unit

p=3 unit

h= ?

by Pythagoras theorem:-

h² = p²+b²

h² = 1²+3²

h = √10

now,

sin = p/h = 3/√10

cos = b/h = 1/√10

tan = p/b =3/1 = 3

cosec = 1/sin =√10/3

sec = 1/ cos =√10/1 = √101/

finding:

3 cos( theta) - 4sin(theta)\div 5sin(theta) + 4cos(theta)3cos(theta)−4sin(theta)÷5sin(theta)+4cos(theta)

=> 3(1/√10) -4 (3/√10)

5(3/√10)+4(1/√10)

=>3/√10 - 12/√10

15/√10 + 4/√10

=>-9/√10

19/√10

=>-9/19