Question

if cos 9a = sin a and 9a < 90 degrees, then the value of tan 5a is :​

Answer 1

Answer:

1

Step-by-step explanation:

Cos 9A = Sin A

=> Cos 9A = Cos(90 - A)  (∵ Sinθ = Cos(90 - θ) )

=> 9A = 90° - A

=> 10A = 90

=> A = 9°

Tan5A = Tan 5 * 9° = Tan 45° = 1

Answer 2

Answer:

Step-by-step explanation:

Cos (90 - β) = Sin β

Cos α = Sin β

(α = 90 - β)

Cos 9a = Sin a

α = 9a; β = a

(90 - a) = 9a

90 = 9a + a

90 = 10a

a = 9

Cos 81 = Sin 9

Tan 5a = (Sin 5a)/ (Cos 5a)

Tan 5(9) = Sin 5(9) / Cos 5(9)

Tan 45 = Sin 45 / Cos 45

Sin (90 - 45) Cos 45

Sin 45 = Cos 45

Therefore,

Sin 45/Cos 45 = 1

So,

Tan 45 = 1