Question 67

If $$3\cos^2x-2\sin^2x=-0.75$$ and $$0^{0} \leq x\leq90^{0}$$,then x = ?

Solution

Given, $$3\cos^2x-2\sin^2x=-0.75$$
=> $$3(1-sin^2x)-2sin^2x = -0.75$$
=> $$3-3sin^2x-2sin^2x = -0.75$$
=> $$3-5sin^2x = -0.75$$
=> $$5sin^2x = 3.75$$
=> $$sin^2x = 0.75$$
=> $$sin^2x = \dfrac{3}{4}$$

=> $$sin x = \dfrac{\sqrt{3}}{2}$$

=> $$x = 60^\circ$$

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RRB ALP 31st Aug 2018 Shift-3

If $$3\cos^2x-2\sin^2x=-0.75$$ and $$0^{0} \leq x\leq90^{0}$$,then x = ?

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