Question 32

The sum of all solutions of the equation $$4 \sin^2 x - 4 \cos x = 1$$ in the interval $$[0, 2\pi]$$ is

Solution

$$4 \sin^2 x - 4 \cos x = 1$$

=> $$4\left(1-\cos\ ^2x\right)-4\cos x-1=0$$

=> $$4\cos\ ^2x+4\cos x+1=4$$

$$\left(2\cos x+1\right)^2=2^2$$

$$2\cos x+1=\pm\ 2$$

$$2\cos x=1\ or\ 2\cos x=-3$$

$$\cos x=\frac{1}{2}\ or\ \cos x=-\frac{3}{2}$$

-3/2 is not possible

Hence x can be $$\frac{\pi}{3}\ or\ 2\pi\ -\frac{\pi}{3}$$

Sum = $$2\pi$$

Create a FREE account and get:

All Quant Formulas and shortcuts PDF
40+ previous papers with solutions PDF
Top 500 MBA exam Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Profit And Loss Questions CAT Arithmetic Questions CAT Coordinate Geometry Questions CAT Quadratic Equations Questions CAT Probability, Combinatorics Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Selection With Condition Questions CAT DI Miscellaneous Questions CAT Coins and Weights Questions CAT Venn Diagrams Questions CAT Charts Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Grammar and Sentence Correction Questions CAT Para Summary Questions CAT Verbal Ability Questions CAT Reading Comprehension Questions CAT Miscellaneous Questions

Follow us on

Boost your Prep!

Download App