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cottheta + cot(pi/4 + theta)=2...

`cottheta + cot(pi/4 + theta)=2`

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`npi +-pi/6`
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If tan (pi cot theta )= cot (pi tan theta) , then show that tan theta= (1)/(4)[ 2 n+ 1+- sqrt(4n^(2)+4n-15)] , where n gt 1 or n lt -2 .

If tan (pi cos theta) = cot (pi sin theta), then the valus of cos (theta -(pi)/(4)) are-

Show that the value of each of the following expressions is independent of theta [cot (pi/4 - theta) - 1] (cot theta -1)

(i) If sin(pi/2costheta) = cos(pi/2 sin theta) , show that, +- cos(theta + pi/4) =(4n+1)/sqrt(2) where n= any integer. (ii) If tan(pi cos theta) = cot(pi sin theta) , prove that, cos(theta - pi/4) = (2n+1)/(2sqrt(2)), n=0, -1,1,-2,2 ,............

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

If sin (pi cot theta)= cos (pi tan theta) and n is an integer, then prove that the value of cot 2 theta is of the form (1)/(4) +k .

If tan (pi cos theta)= cot (pi sin theta) , show that cos (theta-(pi)/(4))=+- (1)/(2sqrt(2))

If sin ( pi cos theta ) = cos (pi sin theta ), , then show that theta =+- (1)/(2) sin ^(-1)""(3)/(4)

If sin ((pi)/(4) cot theta)= cos ((pi)/(4) tan theta), then the general value of theta is-

Let theta in ( 0, pi/4) and t_1 = (tan theta)^(tan theta) , t_2 = (tan theta)^(cot theta), t_3 = ( cot theta)^(tan theta), t_4=(cot theta)^(cot theta) , then

CHHAYA PUBLICATION-GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS -Long Answer type questions
  1. 4 cosx + 5 sinx = 5, given tan51^(@) 21' = 5/4

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  2. 1 + sin^(2) theta = 3sintheta costheta, given cot 18^(@) 26'=3

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  3. tan theta + sec theta = sqrt(3)

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  4. (1-tantheta)(1+sin 2theta) = (1+tantheta)

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  5. (sec theta +1) = (2+sqrt(3))tantheta (0 lt theta lt 2pi)

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  6. cottheta + cot(pi/4 + theta)=2

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  7. cot^(3)theta + 6 "cosec"2theta - 8 "cosec"^(3)2theta=0

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  8. tan^(2)2x + cot^(2)2x + 2tan 2x + 2 cot 2x=6

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  9. sin^(3)x +sin^(3)(x-(2pi)/3) +sin^(3)(x+(2pi)/3)=0

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  10. 2tanx = sin4x - 2sin2x cos2x tan^(2)x

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  11. sin3alpha = 4 sin alpha sin(x+alpha)sin(x-alpha)

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  12. cos3xcos^(3)x + sin3x sin^(3)x=0

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  13. (i) Solve: cos(2x + 3y)=1/2, cos(3x+2y) = sqrt(3)/2 (ii) If 0 lt x l...

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  14. Show that the following two equations represent the same set of angles...

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  15. (i) If sin(pi/2costheta) = cos(pi/2 sin theta), show that, +- cos(thet...

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  16. If cosecA = cosecB and secA = secB, then prove that, either A=B or the...

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  17. If 16tan^(8)phi = cos 2theta + 3 costheta and 3 cos^(2)phi=2, then fin...

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  18. Solve: 2(sinx -cos2x)-sin2x(1+2sinx) + 2cosx =0

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  19. Prove that the system of equations x-y = (2pi)/3 and cosx + cosy =3/2 ...

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  20. Solve: tanx + tany =1, x+y=pi/4

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