Question

Given that sinø =a÷b
, find the wake of tanø.​

Answer 1

Answer:

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Step-by-step explanation:

Given, sinθ=

b

a

⇒ cosθ=

1−sin

2

θ

=

1−

b

2

a

2

=

b

2

b

2

−a

2

=

b

b

2

−a

2

tanθ=

cosθ

sinθ

=

b

b

2

−a

2

a/b

=

b

2

−a

2

Answer 2

Step-by-step explanation:

Given,

sin∅ = a/b

let,

sin∅ = opposite side/hypotenuse = a/b

let,

AC = b, BC = a, AB = ?,

Now,

According to PHYTHAGAROUS THEROM,

(Hypotenuse)² = (side)² + (side)²

(AC)² = (AB)² + (BC)²

(b)² = (AB)² + (a)²

b² = (AB)² + a²

b²-a² = (AB)²

√b²-a² = AB

:. AB = √b²-a².

Now consider,

tan∅ = opposite side/adjacent side = BC/AB

= a/√b²-a².