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If x/(costheta)=y/(cos(theta-(2pi)/3))=z...

If `x/(costheta)=y/(cos(theta-(2pi)/3))=z/(cos(theta+(2pi)/3))` then x+y+z is

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If x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3) show that xy + yz+ zx = 0

If x sin theta = y sin ( theta + (2pi)/3) = z sin ( theta+ (4pi)/3), then the value of xy+yz+zx will be-

By using properties of determinats. Prove that- |(sintheta,costheta,sin2theta),(sin(theta+(2pi)/3), cos(theta + (2pi)/3) ,sin(2theta + (4pi)/3)),(sin(theta-(2pi)/3) ,cos(theta - (2pi)/3), sin (2theta - (4pi)/3))|= 0

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Prove that for all values of theta , |{:(sintheta,costheta,sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2pi)/(3)),sin(2theta+(4pi)/(3))),(sin(theta-(2pi)/(3)),cos(theta-(2pi)/(3)),sin(2theta-(4pi)/(3))):}|=0

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If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta and if |[a,b,c],[b,c,a],[c,a,b]|=0 then a. theta=2kpi, k in Z b. theta=(2k+1)pi, k in Z c. theta=(4k+1)pi, k in Z d. none of these

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sin(x+20^0)=2sinxcos40^0,where in (0,pi/2), then which of the follo...

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  2. cosθ/ (1-tanθ) + sinθ/ (1−cotθ) is equals to ​

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  3. If x/(costheta)=y/(cos(theta-(2pi)/3))=z/(cos(theta+(2pi)/3)) then x+y...

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  4. Prove that : (cosecθ−cotθ)^2 = (1-cosθ)/(1+cosθ) ​

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  5. Let (sin(theta-alpha))/("sin"(theta-beta))=a/b a n d(cos(theta-alpha)...

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  6. (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

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  7. The value of expression (2(sin1^0+sin2^0+sin3^0+...+sin89^0))/(2(cos1...

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  8. If sintheta1sintheta2-costheta1costheta2+1=0, then the value of tan((t...

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  9. on a cartesian plane, draw a line segment XY parallel to x-axis at a d...

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  10. In triangle A B C , prove that sin(A/2)+sin(B/2)+sin(C/2)lt=3/2dot H...

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  11. If x1 and x2 are two distinct roots of the equation acosx+bsinx=c , ...

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  12. (sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a)sec(alp...

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  13. If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbe...

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  14. If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany...

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  15. Suppose A and B are two angles such that A , B in (0,pi) and satisfy s...

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  16. If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be

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  17. The absolute value of the expression tan(pi/(16))+tan((5pi)/(16))+tan(...

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  18. Prove that: (sin2theta)/(1+cos2theta)=tantheta

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  19. If A and B are acute positive angles satisfying the equations 3 sin^(2...

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  20. The roots of the equation 4x^2-2sqrt(5)x+1=0,a r e

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