Home
Class 12
MATHS
The general solution of the trigonometri...

The general solution of the trigonometric equation `sinx+cosx=1` is given by 1.x=2npi,n=0,+-1,+-2`.. 2. x=2npi+pi/2; n=0,+-1,+-2, dot` 3. x='npi'+(-1)^n (pi/4)-(pi/4) ,n=0,+-1,+-2, ` 4.`none of these`

A

`x=2npi,n = 0, pm1, pm2`…..

B

`x= 2npi + pi//2, n = 0,pm1,pm 2`……

C

`x= npi+(-1)^(n)(pi)/(4).(pi)/(4),n = 0,pm 1,pm 2`……

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Given `sin x + cos x = 1`
On dividing and multiplying each terms by `sqrt(2)`, we get
`(1)/(sqrt(2)) sin x +(1)/(sqrt(2)) cos x = (1)/(sqrt(2))`
`rArr sin x cos.(pi)/(4) = cos x sin .(pi)/(4) = (1)/(sqrt(2))`
`rArr sin (x+(pi)/(4)) = sin((pi)/(4))`
`rArr x + (pi)/(4) = npi + (-1)^(n) (pi)/(4)`
`rArr x = npi+(-1)^(n) (pi)/(4)-(pi)/(4), n in I`
Promotional Banner

Similar Questions

Explore conceptually related problems

The general solution of the equation sin^(100)x-cos^(100)x=1 is 2npi+pi/3,n in I (b) n pi+pi/2,n in I npi+pi/4,n in I (d) 2npi=pi/3,n in I

The general solution of cosxcos6x=-1 is x=(2n+1)pi,n in Z x=2npi,n in Z x=npi,n in Z (d) none of these

The number of solution of the equation |2sinx-sqrt(3)|^(2cos^2 x-3cosx+1)=1in[0,pi] is 2 (b) 3 (c) 4 (d) 5

The general values of theta satisfying the equation 2sin^2theta-3sintheta-2=0 is (n in Z)dot npi+(-1)^npi/6 (b) npi+(-1)^npi/2 npi+(-1)^n(5pi)/6 (d) npi+(-1)^n(7pi)/6

A general solution of tan^2theta+cos2theta=1 is (n in Z) npi=pi/4 (b) 2npi+pi/4 npi+pi/4 (d) npi

The solutions of the equation 1+(sinx-cosx)sinpi/4=2cos^2(5x)/2 is/are x=(npi)/3+pi/8, n in Z x=(npi)/2+(5pi)/(16), n in Z x=(npi)/3+pi/4, n in Z x=(npi)/2+(7pi)/8, n in Z

The general solution of the equation sinx-3sin2x+sin3x=cosx-3cos2x+cos3x is (n in Z) npi+pi/8 (b) (npi)/2+pi/8 (-1)^n(npi)/2+pi/8 (d) 2npi+cos^(-1)2/3

The number of solutions of the equation 1+cosx+cos2x+sinx+sin2x+sin3x=0, which satisfy the condition pi/2<|3x-pi/2|lt=pi is

Which of the following is not the solution of the equation sin5x=16sin^5x(n in Z)? npi (b) npi+pi/6 (c) npi-pi/6 (d) none of these

Find the number of solution of the equation 1+e^(cot^2 x )=sqrt(2|sinx|-1)+(1-cos2x)/(1+sin^4x) for x in (0,5pi)dot