Question

5x=sinx and 5/x =cosx then x2+1/x2=

Answer 1

Given,

• $5x=\sin x$

• $\dfrac{5}{x}=\cos x$

We have,

$\longrightarrow\sin^2x+\cos^2x=1$

Putting values for each,

$\longrightarrow(5x)^2+\left(\dfrac{5}{x}\right)^2=1$

$\longrightarrow25x^2+\dfrac{25}{x^2}=1$

$\longrightarrow25\left(x^2+\dfrac{1}{x^2}\right)=1$

Dividing by 25, we get,

$\longrightarrow\underline{\underline{x^2+\dfrac{1}{x^2}=\dfrac{1}{25}}}$

Hence 1/25 is the answer.

_________________________________

Some Trigonometric Identities...

$\longrightarrow \sin^2x+\cos^2x=1$

$\longrightarrow \sec^2x-\tan^2x=1$

$\longrightarrow \csc^2x-\cot^2x=1$

$\longrightarrow\sin(x\pm y)=\sin x\cos y+\cos x\sin y$

$\longrightarrow\cos(x\pm y)=\cos x\cos y\mp\sin x\sin y$

$\longrightarrow\tan(x\pm y)=\dfrac{\tan x\pm\tan y}{1\mp\tan x\tan y}$