Question

Solve sin^2 theta-2 cos +1/4=
0 for the general solution​

Answer 1

Answer:

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Answer 2

Answer:

Ф = 2 n π ± π / 3 where n € I .

Step-by-step explanation:

Given :

sin² Ф - 2 cos Ф + 1 / 4

We have value of sin² Ф = 1 - cos² Ф

1 - cos² Ф - 2 cos Ф + 1 / 4 = 0

- cos² Ф - 2 cos Ф + 5 / 4 = 0

cos² Ф  + 2 cos Ф - 5 / 4 = 0

4 cos² Ф + 8 cos Ф - 5 = 0

By splitting mid term we get :

( 2 cos Ф + 5 ) ( 2 cos Ф - 1 ) = 0

Value of cos Ф as :

( 2 cos Ф + 5 ) = 0

2 cos Ф = - 5

cos Ф = - 5 / 2

Since value of cos Ф is vary - 1 to + 1 .

So first one is incorrect :

When ( 2 cos Ф - 1 ) = 0

2 cos Ф = 1

cos Ф = 1 / 2

cos Ф = cos π / 3

Ф = 2 n π ± π / 3 where n € I .

Therefore we get general solution of sin² Ф - 2 cos Ф + 1 / 4 .