Q28 / 83 · NTA Abhyas (JEE Main) 2020 · Mathematics · Trigonometric Equations

The sum of all the solutions in $[0,100]$ for the equation $\sin π x + \cos π x = 0$ is

A
$2550$
Correct answer
B
$5025$
C
$2525$
D
$5050$

Solution

\sin π x + \cos π x = 0

\tan π x = - 1 = t a n \frac{3 π}{4}

π x = n π + \frac{3 π}{4} \Rightarrow x = n + \frac{3}{4}

Given,

x \in [0,100],

hence

n

will range from

0

to

99 .

x

will be

\frac{3}{4}, \frac{7}{4}, \frac{11}{4}, . . . . ., \frac{399}{4}

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

= 50 [\frac{6}{4} + 99 \times 1] = 5025

Hence, the correct answer is option: 'B'.

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