Question

7sinA+24cosA=25 find the value of tanA. plz help

Answer 1

7 Sin A + 24 Cos A = 25 ......(1)

r = √ ( 7 ² + 24 ² ) = √ ( 625 ) = 25

Divide equation (1) by 25 both sides,

( 7 / 25 ) Sin A + ( 24 / 25 ) Cos A = 1 .....(2)

Take 7 / 25 = Sinα , 24 / 25 = Cosα

cot α = cos α / sin α = 24 / 7

Cot α = 24 / 7

(2) becomes,

Sin α Sin A + Cos α Cos A = 1

Cos ( α + A ) = 1

Cos ( α +A ) = Cos 90⁰

α + A = 90⁰

A = 90 - α

tan A = tan ( 90 - α )

tan A = Cot α = 24 / 7