If cos[(3pi)/4 -theta]-sin[(3pi)/4 +thet...

If `cos[(3pi)/4 -theta]-sin[(3pi)/4 +theta]=1`,find `theta`

Text Solution

Verified by Experts

The correct Answer is:

`pi/12`

Topper's Solved these Questions

TRIGONOMETRY
PREMIERS PUBLISHERS|Exercise IDENTITY|14 Videos
TRIGONOMETRY
PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 3.1|23 Videos
SETS,RELATIONS AND FUNCATIONS
PREMIERS PUBLISHERS|Exercise II. Choose the correct option for the following. (M.C.Q)|35 Videos
TWO DIMENSIONAL ANALYTICAL GEOMETRY
PREMIERS PUBLISHERS|Exercise PROBLEM FOR PRACTICE (CHOOSE THE CORRECT OPTION)|28 Videos

Similar Questions

Explore conceptually related problems

Prove that tan ((pi)/(4) + theta)- tan ((pi)/(4) - theta) = 2 tan 2 theta .

Prove that sin (pi + theta) = - sin theta

If sin ((pi)/(4) cot theta) = cos ((pi)/(4) tan theta ) , then theta =

Find number of solutions of equation sin^(2) theta- 4/(sin^(3) theta-1)=1- 4/(sin^(3) theta-1), theta in [0, 6pi] .

Prove that tan ((pi)/(4) + theta) tan ((3pi)/(4) + theta) = -1

Solve 7 cos^(2) theta+3 sin^(2) theta=4 .

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of (tan^(2)""(pi)/(7) + tan^(2)""(2pi)/(7) + tan^(2)""(3pi)/(7))xx (cot^(2)""(pi)/(7) + cot^(2)""(2pi)/(7) + cot^(2)""(3pi)/(7)) is

To find the sum sin^(2) ""(2pi)/(7) + sin^(2)""(4pi)/(7) +sin^(2)""(8pi)/(7) , we follow the following method. Put 7theta = 2npi , where n is any integer. Then " " sin 4 theta = sin( 2npi - 3theta) = - sin 3theta This means that sin theta takes the values 0, pm sin (2pi//7), pmsin(2pi//7), pm sin(4pi//7), and pm sin (8pi//7) . From Eq. (i), we now get " " 2 sin 2 theta cos 2theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta (1-2 sin^(2) theta)= sin theta ( 4sin ^(2) theta -3) Rejecting the value sin theta =0 , we get " " 4 cos theta (1-2 sin^(2) theta ) = 4 sin ^(2) theta - 3 or 16 cos^(2) theta (1-2 sin^(2) theta)^(2) = ( 4sin ^(2) theta -3)^(2) or 16(1-sin^(2) theta) (1-4 sin^(2) theta + 4 sin ^(4) theta) " " = 16 sin ^(4) theta - 24 sin ^(2) theta +9 or " " 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta -7 =0 This is cubic in sin^(2) theta with the roots sin^(2)( 2pi//7), sin^(2) (4pi//7), and sin^(2)(8pi//7) . The sum of these roots is " " sin^(2)""(2pi)/(7) + sin^(2)""(4pi)/(7) + sin ^(2)""(8pi)/(7) = (112)/(64) = (7)/(4) . The value of (tan^(2)""(pi)/(7) + tan^(2)""(2pi)/(7) + tan^(2)""(3pi)/(7))/(cot^(2)""(pi)/(7) + cot^(2)""(2pi)/(7) + cot^(2)""(3pi)/(7)) is

PREMIERS PUBLISHERS-TRIGONOMETRY-CHOOSE THE CORRECT ANSWER

If cos[(3pi)/4 -theta]-sin[(3pi)/4 +theta]=1,find theta
Text Solution
|
1/(cos80^o) -sqrt3/(sin80^o ) =
Text Solution
|
If cos28^o +sin28^o =k^3,then cos17^o is equal
Text Solution
|
The maximum value of 4 sin^(2) x + 3 cos^(2) x + sin ""(x)/(2) + cos""...
Text Solution
|
(1 + cos"" (pi)/(8))(1 + cos"" (3pi)/(8)) (1 + cos"" (5pi)/(8))(1 + co...
Text Solution
|
If pi lt 2 theta lt (3pi)/(2), then sqrt(2 + sqrt( 2 + 2 cos 4 theta))...
Text Solution
|
If tan40^o =lambda, then(tan140^o -tan130^o )/(1+tan140^o tan130^o)=
Text Solution
|
cos1^(@)+cos2^(@)cos3^(@)...+cos179^(@)" is "
Text Solution
|
Letf(4)(x) = (1)/(k) [ sin^(k) + cos^(k) x ] where x in RR and k ge1. ...
Text Solution
|
Which of the following is not true?
Text Solution
|
cos 2theta cos 2phi + sin^(2) (theta - phi ) - sin^(2) ( theta + phi) ...
Text Solution
|
(sin(A - B))/(cos A cos B) + (sin (B - C))/( cos B cos C) + (sin(C - A...
Text Solution
|
If cos ptheta + cos qtheta = 0 and if p ne q, then theta is equal to (...
Text Solution
|
If tan alpha and tan beta are the roots of x^(2) + ax + b = 0, then (s...
Text Solution
|
In a triangle ABC, sin^(2)A + sin^(2)B + sin^(2)C = 2, then the triang...
Text Solution
|
If f(theta) = |sin theta| + |cos theta|,theta in RR, then f(theta) is ...
Text Solution
|
(cos 6x + 6 cos 4x + 15 cos 2x + 10)/(cos 5x + 5 cos 3x + 10 cos x ) i...
Text Solution
|
The triangle of maximum area with constant perimeter 12m
Text Solution
|
A wheel is spinning at 2 radians/second. How many seconds will it take...
Text Solution
|
If sin alpha + cos alpha = b, then sin 2alpha is equal to
Text Solution
|
In a DeltaABC, if (i)sin (A)/(2) sin"" (B)/(2) sin"" (C )/(2) gt 0 (...
Text Solution
|