NDA 2017 Paper 1 | Trigonometric Angles and Equations Question 32 | Mathematics

If $$K = \sin \left( {{\pi \over {18}}} \right)\sin \left( {{{5\pi } \over {18}}} \right)\sin \left( {{{7\pi } \over {18}}} \right)$$, then what is the value of K?

$${1 \over 2}$$

$${1 \over 4}$$

$${1 \over 8}$$

$${1 \over 16}$$

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

The expression $${{\sin \alpha + \sin \beta } \over {\cos \alpha + \cos \beta }}$$ is equal to

$$\tan \left( {{{\alpha + \beta } \over 2}} \right)$$

$$\cot \left( {{{\alpha + \beta } \over 2}} \right)$$

$$\sin \left( {{{\alpha + \beta } \over 2}} \right)$$

$$\cos \left( {{{\alpha + \beta } \over 2}} \right)$$

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If $$\sin \theta = 3\sin (\theta + 2\alpha )$$, then the value of tan ($$\theta$$ + $$\alpha$$) + 2 tan$$\alpha$$ is equal to

$$-$$ 1

NDA 2017 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the value of tan18$$^\circ$$ ?

$${{\sqrt 5 - 1} \over {\sqrt {10 + 2\sqrt 5 } }}$$

$${{\sqrt 5 - 1} \over {\sqrt {10 + \sqrt 5 } }}$$

$${{\sqrt {10 + 2\sqrt 5 } } \over {\sqrt 5 - 1}}$$

$${{\sqrt {10 + \sqrt 5 } } \over {\sqrt 5 - 1}}$$

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