Question

2sin^2theta+5costheta=4 find cos theta

Answer 1

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Answer 2

hello users....

solution:-
we know that:
sin²x = 1 - cos²x 

here
2 sin²θ + 5 cosθ = 4 

=> 2 ( 1 - cos²θ) + 5 cos θ = 4 

=> 2 - 2 cos²θ + 5 cos θ  = 4 

=> 2 cos²θ - 5 cosθ  + 2 = 0

now,
Let 
cos θ = x 

Here 
 => 2x² - 5x + 2 = 0 

=> 2x² - 4x - 1x + 2 = 0 

=> 2x( x - 2) - 1(x - 2) = 0 

=> (2x - 1 ) (x - 2) = 0 

=> x = 1 / 2  or x = 2 

here,
 x = cosθ = 1 / 2  Answer 

Here,
value x = 2 is neglected.

because 
cos θ is can't equal to 2

# Hope it helps :)