What is the general solution of ^ 100 x- ^ 100 x=1 ? where n is an integer.

Correct answer: A. n π Since, ^2 x ∈[0,1] ^ 100 x ∈[0,1] and ^2 x ∈[0,1] ^ 100 x ∈[0,1] Hence, ^ 100 x- ^ 100 x=1 is only possible when aligned & ^ 100 x=1 & ^2 x=1 x=n π ± 0 x=n π aligned

NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Trigonometric Equations

NDA 2024 · Mathematics · Trigonometric Equations

What is the general solution of ^ 100 x- ^ 100 x=1 ? where n is an...

What is the general solution of

\cos ^{100} x-\sin ^{100} x=1

? where

n

is an integer.

Options

A $n \pi$
B $(2 n+1) \pi$
C $2 n \pi$
D $(2 n+1) \frac{\pi}{2}$

Correct answer

A. $n \pi$

Step-by-step solution

Since,

\cos ^2 \mathrm{x} \in[0,1] \Rightarrow \cos ^{100} \mathrm{x} \in[0,1]

and

\sin ^2 x \in[0,1] \Rightarrow \sin ^{100} x \in[0,1]

Hence,

\cos ^{100} \mathrm{x}-\sin ^{100} \mathrm{x}=1

is only possible when

\begin{aligned} & \cos ^{100} x=1 \\ & \Rightarrow \cos ^2 x=1 \Rightarrow x=n \pi \pm 0 \Rightarrow x=n \pi \end{aligned}

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