Request a call back

if cot^-(-cot5x)=tan^-( cotx),0
Asked by ajaysir635 | 26 Dec, 2023, 12:00: PM

Let cot-1 ( - cot 5x ) = tan-1 ( cot x ) = α

from LHS  ,  cot-1 ( - cot 5x ) =  α

cot( α ) = - cot(5x) ........................... (1)

Similarly from RHS

tan-1 ( cot x ) = α

tan ( α ) = cot x  ..........................(2)

From eqn.(1) and (2) , we get

cot ( α ) tan (α ) = - cot(5x) cot(x) = 1

hence we get, cos(5x)cos(x) + sin(5x) sinx = 0

cos( 5x -x ) = cos(4x) = 0

cos(4x) = cos[ (2n+1) (π / 2 ) ] , where n = 0, 1,  2 ........ etc

4x = (2n+1) (π / 2 )

x = (2n+1) (π / 8 )

if n = 0 , then x = (π / 8 )

if n =1 , then x = (3 π ) / 8

Answered by Thiyagarajan K | 26 Dec, 2023, 02:26: PM
JEE main - Maths
Asked by sandipan.sarma6 | 14 Apr, 2024, 10:27: AM
JEE main - Maths
Asked by pranavpatil7386 | 07 Feb, 2024, 08:54: PM
JEE main - Maths
Asked by ajaysir635 | 26 Dec, 2023, 12:00: PM
JEE main - Maths
Asked by akshravirash | 21 Dec, 2023, 11:07: PM
JEE main - Maths
Asked by antarshekhawat18 | 25 May, 2022, 10:32: AM
JEE main - Maths