Question 69

If Ɵ is positive acute angle and $$7cos^{2}$$Ɵ + 3 $$sin^{2}$$ Ɵ = 4, then the value of θ is

Solution

Expression : $$7cos^{2}$$Ɵ + 3 $$sin^{2}$$ Ɵ = 4

Using, $$sin^2\theta+cos^2\theta=1$$

=> $$7cos^2\theta+3(1-cos^2\theta)=4$$

=> $$7cos^2\theta+3-3cos^2\theta=4$$

=> $$4cos^2\theta=4-3=1$$

=> $$cos^2\theta=\frac{1}{4}$$

=> $$cos\theta=\sqrt{\frac{1}{4}}=\frac{1}{2}$$

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

=> $$\theta=60^\circ$$

=> Ans - (A)

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