NDA 2016 Paper 2 | Trigonometric Angles and Equations Question 7 | Mathematics

If $$\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} + \sin {\theta _4} = 4$$, then what is the value of $$\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} + \cos {\theta _4}$$ ?

NDA 2016 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

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$$^\circ$$ ?

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

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

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

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

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