Question

if sin$+cos$=1, find value of sin$/sec$ (theta=$)​

Answer 1

Answer:

0

Step-by-step explanation:

we know (sin$)^2 + (cos$)^2 = 1

taking (cos$)^2 to right hand side.

then, (sin$)^2 = 1 - (cos$)^2

now taking square root on both sides

sin$ = sqrt[1 - (cos$)^2]

Now putting this value of sin$ in given equation

sqrt[1 - (cos$)^2] + cos$ = 1

now taking cos$ to RHS

sqrt[1 - (cos$)^2] = 1 - cos$

Taking square on both sides

1 - (cos$)^2 = (1 - cos$)^2

1 - (cos$)^2 = 1 + (cos$)^2 - 2cos$

taking all the values on one side

2(cos$)^2 - 2cos$ = 0

this will become

2cos$(cos$ - 1) = 0

This gives us value of cos$ = 0 and cos$ = 1

Now we will solve this for both these values

for cos$ = 0

sin$/sec$ or sin$.cos$ = 1*0 = 0

for cos$ = 1

sin$.cos$ = 0*1 = 0