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Prove that: 3(sintheta-costheta)^4+6(sin...

Prove that: `3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)-13=0.`

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RD SHARMA ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that: s e c^2theta+cos e c^2thetageq4 .

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  2. Given that: (1+cosalpha)(1+cosbeta)(1+cosgamma)=(1-cosalpha)(1-cosbeta...

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  3. Prove that: 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta...

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  4. Prove that: 2s e c^2theta-s e c^4theta-2cos e c^2theta+cos e c^4theta=...

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  5. If A lies in second quadrant and 3tanA+4=0, then the value of 2cotA-5c...

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  6. Is the following inequality correct? sin1^0> sin1

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  7. If f(x)=cos^2x+s e c^2x ,t h e n (a) f(x)<1 (b) f(x)=1 (c) 2ltf(x)<...

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  8. If sectheta=x+1/(4x), then s e ctheta+t a ntheta= (a) x ,1/x (b) 2x ...

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  9. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if (a)x+y!=0 (b)...

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  10. If cos e ctheta+cottheta=(11)/2 , then t a ntheta= (21)/(22) (b) (15...

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  11. If (3pi)/4 lt alpha lt pi, then sqrt(2cotalpha+1/(sin^2alpha)) is equ...

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  12. If x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+...

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  13. If sintheta+costheta=0 and theta lies in the fourth quadrant, find si...

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  14. Prove that: sqrt(1-sintheta)/(1+s intheta)+sqrt((1+sintheta)/(1-s inth...

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  15. Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

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  16. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)} =cot^2x

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  17. If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+...

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  18. If tanx=(b)/(a), then find the value of sqrt((a+b)/( a-b ))+sqrt((a-b)...

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  19. Find the values of the following trigonometric ratios. (1) cos e c390^...

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  20. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

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