NDA 2018 Paper 1 | Trigonometric Angles and Equations Question 50 | Mathematics

If x, x $$-$$ y and x + y are the angles of a triangle (not an equilateral triangle) such that tan (x $$-$$ y), tan x and tan (x + y) are in GP, then what is x equal to?

$${\pi \over 4}$$

$${\pi \over 3}$$

$${\pi \over 6}$$

$${\pi \over 2}$$

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

ABC is a triangle inscribed in a circle with centre O. Let $$\alpha$$ = $$\angle$$BAC, where 45$$^\circ$$ < $$\alpha$$ < 90$$^\circ$$. Let $$\beta$$ = $$\angle$$BOC. Which one of the following is correct?

$$\cos \beta = {{1 - {{\tan }^2}\alpha } \over {1 + {{\tan }^2}\alpha }}$$

$$\cos \beta = {{1 + {{\tan }^2}\alpha } \over {1 - {{\tan }^2}\alpha }}$$

$$\cos \beta = {{2\tan \alpha } \over {1 + {{\tan }^2}\alpha }}$$

$$\sin \beta = 2{\sin ^2}\alpha $$

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If $${{\sin (x + y)} \over {\sin (x - y)}} = {{a + b} \over {a - b}}$$, then what is $${{\tan x} \over {\tan y}}$$ equal to?

$${a \over b}$$

$${b \over a}$$

$${{a + b} \over {a - b}}$$

$${{a - b} \over {a + b}}$$

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If sin$$\alpha$$ + sin$$\beta$$ = 0 = cos$$\alpha$$ + cos$$\beta$$, where 0 < $$\beta$$ < $$\alpha$$ < 2$$\pi$$, then which one of the following is correct?

$$\alpha$$ = $$\pi$$ $$-$$ $$\beta$$

$$\alpha$$ = $$\pi$$ + $$\beta$$

$$\alpha$$ = 2$$\pi$$ $$-$$ $$\beta$$

2$$\alpha$$ = $$\pi$$ + 2$$\beta$$

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