Question

theta +phy=60degree.show that sin(120-theta)=cos(30-phy)​

Answer 1

Answer:

Hope it helps you

Step-by-step explanation:

We can write ,

cos (30° - θ) = cos { 90° -(60° + θ)}= sin(60°+ θ)

Now, Sin(60° + θ) - cos(30° - θ)

= Sin(60° + θ) - sin(60°+ θ)

= 0

Answer 2

Step-by-step explanation:

Given:

Ф + θ = 60°

To prove that: \sin (120-\theta)sin(120−θ) = \cos(30-\phi)cos(30−ϕ) .

L.H.S. = \sin (120-\theta)sin(120−θ)

∵ Ф + θ = 60°

⇒ θ = 60°  - Ф

= \sin (120-(60-\phi))sin(120−(60−ϕ))

= \sin (120-60+\phi)sin(120−60+ϕ)

= \sin (60+\phi)sin(60+ϕ)

Using the trigonometric identity:

\cos AcosA = \sin (90-A)sin(90−A)

= \cos (90-60-\phi)cos(90−60−ϕ)

= \cos(30-\phi)cos(30−ϕ)

= R.H.S., proved.

Thus, \sin (120-\theta)sin(120−θ) = \cos(30-\phi)cos(30−ϕ) , proved.