Question

If 4cosa +3sina =5 find the value of Tana

Answer 1

$\bf{hey}$

Given :- 4cosa + 3sina = 5

Divided by cosa on both side

then , we get

$\frac{4cosa + 3sina}{cosa} = \frac{5}{cosa}$

squaring on both side

=> (4 + 3 tana )²= (5seca)²

=> 16 + 9 tan²a + 24tana = 25 ( 1 + tan²a )

=> 25tan²x - 9tan²a - 24tana + 25 - 16 =0

=> 16tan²a - 24tana + 9 =0

let tana = x

since, it will be in quadratic form

=> 16x² + 24 x + 9 =0

=> 16x²- 12-12x + 9=0

=> 4x ( 4x - 3 ) - 3( 4x -3 ) =0

=> (4x -3) ( 4x -3 ) = 0

=> 4x - 3 = 0

x = 3/4

or , ( 4x - 3) = 0

x = 3/4

hence, tana = 4/3

{tan(a) = 4/3 Answer}
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Hope it helps you

@Rajukumar