Question -
Answer -
Let f(x) = sin 100° – sin 10°
Dividing And multiplying by √(12 + 12)i.e. by √2,
f(x) = √2(1/√2 sin 100o – 1/√2 sin 10o)
f(x) = √2(cos π/4 sin (90+10)o – sinπ/4 sin 10o) (since, 1/√2 = cos π/4 and 1/√2 = sin π/4)
f(x) = √2(cos π/4 cos 10o – sin π/4sin 10o)
We know that cos A cos B – sin A sin B = cos (A + B)
f(x) = √2 cos (π/4 + 10o)
∴ f(x) = √2 cos 55°