Number of integral value (s) of 'p' for which equation 99cos 2θ - 20sin 2θ = 2

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Trigonometrical Equations

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The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta - 20\sin 2\theta = 20p + 35$ , will have a solution is

A

$8$

B

$9$

C

$10$

D

$11$

Solution

$-101 \leq 99 \cos 2 \theta-20 \sin 2 \theta \leq 101$

$\therefore $ Given equation will have a solution,

if $-101 \leq 20 p+35 \leq 101 \Rightarrow-6.8 \leq p \leq 3.3$

Hence number of integral value$(s)$ of $'p'= 10$

Standard 11

Mathematics

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