Find the value of (Sin 75+Sin 15)/(Cos 75+Cos 15)
Answers
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.
.: The value of (Sin75° + Sin15°) - (Cos 75° + Cos15°) is 0.
this is answer hope it's help you

