NDA 2018 Paper 2 | Trigonometric Angles and Equations Question 41 | Mathematics

If $$\sec (\theta - \alpha )$$, $$\sec \theta $$ and $$\sec (\theta + \alpha )$$ are in AP, where cos $$\alpha$$ $$\ne$$ 1, then what is the value of sin²$$\theta$$ + cos$$\alpha$$ ?

$$-$$ 1

$${1 \over 2}$$

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If A + B + C = 180$$^\circ$$, then what is $$\sin 2A - \sin 2B - \sin 2C$$ equal to?

$$-$$4 sin A sin B sin C

$$-$$4 cos A sin B cos C

$$-$$4 cos A cos B sin C

$$-$$4 sin A cos B cos C

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

A is an angle in the fourth quadrant it satisfies the trigonometric equation $$3{(3 - {\tan ^2}A - \cot A)^2} = 1$$. Which one of the following is a value of A?

300$$^\circ$$

315$$^\circ$$

330$$^\circ$$

345$$^\circ$$

NDA 2018 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

What is/are the solution(s) of the trigonometric equation $$\cos ec\,x + \cos x = \sqrt 3 $$ where 0 < x < 2$$\pi$$ ?

$${{5\pi } \over 3}$$ only

$${{\pi } \over 3}$$ only

$$\pi$$ only

$$\pi$$, $${{\pi } \over 3}$$, $${{5\pi } \over 3}$$

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