NDA 2016 Paper 2 | Trigonometric Angles and Equations Question 8 | Mathematics

What is the value of $$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ ?

$${1 \over 2}$$

$${1 \over 2} + {1 \over {2\sqrt 2 }}$$

$${1 \over 2} - {1 \over {2\sqrt 2 }}$$

$${1 \over 8}$$

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If $$x\cos \theta + y\sin \theta = z$$, then what is the value of $${(x\sin \theta - y\cos \theta )^2}$$ ?

$${x^2} + {y^2} - {z^2}$$

$${x^2} - {y^2} - {z^2}$$

$${x^2} - {y^2} + {z^2}$$

$${x^2} + {y^2} + {z^2}$$

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If $$\sin 18^\circ = {{\sqrt 5 - 1} \over 4}$$, then what is the value of sin81$$^\circ$$ ?

$${{\sqrt {3 + \sqrt 5 } + \sqrt {5 - \sqrt 5 } } \over 4}$$

$${{\sqrt {3 + \sqrt 5 } + \sqrt {5 + \sqrt 5 } } \over 4}$$

$${{\sqrt {3 - \sqrt 5 } + \sqrt {5 - \sqrt 5 } } \over 4}$$

$${{\sqrt {3 + \sqrt 5 } - \sqrt {5 - \sqrt 5 } } \over 4}$$

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

What is $${{1 - \tan 2^\circ \cot 62^\circ } \over {\tan 152^\circ - \cot 88^\circ }}$$ equal to?

$$\sqrt 3 $$

$$ - \sqrt 3 $$

$$\sqrt 2 - 1$$

$$1 - \sqrt 2 $$

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