Question

Find the value of (Sin 75+Sin 15)/(Cos 75+Cos 15)​

Answer 1

Answer:

According to the question, we have

Firstly, we solve Sin75° + Sin15°

⇒ Sin75° + Sin15° = 2 Sin{(75° + 15°)/2} Cos{(75° – 15°)/2}

⇒ Sin75° + Sin15° = 2 Sin45° Cos30°

⇒ Sin75° + Sin15° = 2 × (1/√2) × (√3/2)

⇒ Sin75° + Sin15° = √3/√2

Now, we solve (Cos75° + Cos15°)

⇒ Cos75° + Cos15° = 2 Cos{(75° + 15°)/2} Cos{(75° – 15°)/2}

⇒Cos75° + Cos15°=2Cos45°Cos30°

⇒ Cos75° + Cos15° = 2 × (1/√2) × (√3/2)

⇒ Cos75°+ Cos15° = √3/√2

So,the value of (Sin75° + Sin15°) – (Cos75° + Cos15°) is

⇒√3/√2 -√3/√2

⇒ 0

∴The value of (Sin75°+Sin15°)–(Cos75°+Cos15°)is 0

As we know Cos(90–A)=SinA

And Sin(90 – A) = CosA

The value of(Sin75°+Sin15°)–(Cos75°+Cos15°)is

⇒Sin75° + Sin15° – Cos75° - Cos15°

⇒Sin75°+Sin(90-75°)–Cos75°-Cos(90-75°)

⇒Sin75°+Cos75° –Cos75° -Sin75°

⇒ 0

∴ The value of (Sin75° + Sin15°) – (Cos75° + Cos15°) is 0.

Answer 2

.: The value of (Sin75° + Sin15°) - (Cos 75° + Cos15°) is 0.

this is answer hope it's help you