Question 178

The value of $$sin^{2}$$ 22° + $$sin^{2}$$ 68° + $$cot^{2}$$ 30° is

Solution

Expression : $$sin^{2}$$ 22° + $$sin^{2}$$ 68° + $$cot^{2}$$ 30°

We know that $$sin(90^{\circ}-\theta) = cos\theta$$

=> $$sin 22^{\circ} = sin (90^{\circ}-68^{\circ}) = cos 68^{\circ}$$

=> $$cos^2 68^{\circ} + sin^2 68^{\circ} + (\sqrt{3})^2$$

=> 1 + 3 = 4

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