1.

Show that sin 100° – sin 10° is positive.

Answer»

Suppose f(x) = sin 100° – sin 10°

On dividing and multiplying by √(12 + 12) i.e. by √2,

f(x) = √2(1/√2 sin 100° – 1/√2 sin 10°)

f(x) = √2(cos π/4 sin (90 + 10)° – sin π/4 sin 10°) (since, 1/√2 = cos π/4 and 1/√2 = sin π/4)

f(x) = √2(cos π/4 cos 10° – sin π/4 sin 10°)

As we know that cos A cos B – sin A sin B = cos (A + B)

f(x) = √2 cos (π/4 + 10°)
∴ f(x) = √2 cos 55°



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