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