Question

If Cosθ = 0.6, show that 5Sinθ – 3Tanθ = 0​

Answer 1

Step-by-step explanation:

Given:-

Cos θ = 0.6

=> Cos θ = 6/10

=> Cos θ = 3/5 ---------(1)

On squaring both sides then

=> Cos^2 θ = (3/5)^2

=> Cos^2 θ = 9/25

On Subtracting above equation from 1

=> 1 - Cos^2 θ = 1 - (9/25)

=> 1 - Cos^2 θ = = (25-9)/25

=>1 - Cos^2 θ = 16/25

We know that

Sin^2 A + Cos^2 A = 1

=> Sin^2 θ = 16/25

=> Sin θ = √(16/25)

=> Sin θ = 4/5---------(2)

Tan θ = Sin θ / Cos θ

From (1)&(2)

=> Tan θ = (4/5)/(3/5)

=> Tan θ = (4/5)×(5/3)

=> Tan θ = 4/3------(3)

Now ,

The value of 5 Sinθ – 3 Tanθ

=> 5 (4/5) - 3(4/3)

=> (5×4)/5 - (3×4)/3

=> (20/5) - (12/3)

=> 4 - 4

=> 0

5 Sinθ – 3 Tanθ = 0

Answer:-

If Cosθ = 0.6 then 5 Sinθ – 3 Tanθ = 0

Used formulae:-

• Sin^2 A + Cos^2 A = 1

• Tan θ = Sin θ / Cos θ