Question

5 sinA-4cos A = 0 then find the value of tanA​

Answer 1

$\green{\large\underline{\sf{Given- }}}$

$\rm :\longmapsto\:5sinA - 4cosA = 0$

$\pink{\large\underline{\sf{To\:Find - }}}$

$\rm :\longmapsto\:tanA$

$\purple{\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}}$

$\purple{\rm\implies \:\boxed{\tt{ \frac{sinx}{cosx} = tanx}}}$

$\blue{\large\underline{\sf{Solution-}}}$

Given that

$\rm :\longmapsto\:5sinA - 4cosA = 0$

$\rm :\longmapsto\:5sinA = 4cosA$

$\rm :\longmapsto\:\dfrac{sinA}{cosA} = \dfrac{4}{5}$

$\rm\implies \:tanA = \dfrac{4}{5}$

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Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1