Question

7 cos square theta + 3 sin square theta is equal to 4 then cos theta is equal to

Answer 1

Here is the solution of question

Answer 2

Answer:

The value of cosФ for the given trigonometrical expression is  $\pm \frac{1}{2}$  

Step-by-step explanation:

Given Trigonometrical function as :

7 cos²Ф + 3 sin²Ф = 4

Let the value of cosФ = x

So, From expression

7 cos²Ф + 3 sin²Ф = 4

∵ sin²Ф + cos²Ф = 1

or, sin²Ф = 1 - cos²Ф

So, 7 cos²Ф + 3 ( 1 - cos²Ф)  = 4

or, 7 cos²Ф + 3  - 3 cos²Ф  = 4

or, 4 cos²Ф  = 4 - 3

or, 4 cos²Ф  = 1

or,  cos²Ф  = $\frac{1}{4}$

∴  cosФ = $\sqrt{\frac{1}{4} }$

i.e cosФ = $\pm \frac{1}{2}$

Hence The value of cosФ for the given trigonometrical expression is  $\pm \frac{1}{2}$  Answer