Question 139

The value of x which satisfies the equation $$2 \csc^{2} 30^{\circ}+x \sin^{2}60^{\circ}-\frac{3}{4}\tan^{2}30^{\circ}=10$$ is

Solution

Remember that
sin 60° = √3/2
cosec 30° = 1/sin 30° = 1/(1/2) = 2
tan 30° = 1/√3

the given equation becomes

2·(2^2) + (3/4) x - (3/4) (1/3) = 10

8 + (3/4) x - 1/4 = 10

multiply by 4

32 + 3x - 1 = 40

3x = 9

x=3

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SSC CGL 2014 Tier 1 26 Oct shift 3

The value of x which satisfies the equation $$2 \csc^{2} 30^{\circ}+x \sin^{2}60^{\circ}-\frac{3}{4}\tan^{2}30^{\circ}=10$$ is

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