Question 96

If 2 cos θ = 2 - sin θ, then what is the value of cos θ?

Solution

Given : $$2cos\theta=2-sin\theta$$

=> $$2cos\theta=2-\sqrt{1-cos^2\theta}$$

=> $$\sqrt{1-cos^2\theta}=2-2cos\theta$$

Squaring both sides,

=> $$(\sqrt{1-cos^2\theta})^2=(2-2cos\theta)^2$$

=> $$1-cos^2\theta=4+4cos^2\theta-8cos\theta$$

Let $$cos\theta=x$$

=> $$5x^2-8x+3=0$$

=> $$5x^2-5x-3x+3=0$$

=> $$5x(x-1)-3(x-1)=0$$

=> $$(5x-3)(x-1)=0$$

=> $$x=cos\theta=1,\frac{3}{5}$$

=> Ans - (A)

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