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If 3t a n At a n B=1, prove that 2cos(A+...

If `3t a n At a n B=1,` prove that `2cos(A+B)=cos(A-B)dot`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. Prove that: sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2)sinA

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  2. Prove that: sin^2A=cos^2(A-B)+cos^2B-2cos(A-B)cosAcosBdot

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  3. If 3t a n At a n B=1, prove that 2cos(A+B)=cos(A-B)dot

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  4. Prove that: tan75^0+cot75^0=4

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  5. If alphaa n dbeta are the solutions of acostheta+bsintheta=c , then ...

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  6. If alpha a n d beta are the solutions of the equation at a ntheta+bs e...

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  7. If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , show that (tanx)/(tany)=a/b .

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  8. If t a n(pi//4+theta)+t a n(pi//4-theta)=a , then t a n^2(pi//4+theta...

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  9. If t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3, then prove that (3tanx-t a n^...

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  10. If theta lies in the first quadrant and costheta=8/(17) , then prove t...

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  11. If tan(A-B)=1,sec(A+B)=2/(sqrt(3)) , then the smallest positive value ...

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  12. If t a nbeta=(nsinalphacosalpha)/(1-nsin^2alpha) , show that tan(alph...

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  13. If A+B=pi/4 , prove that: (1+t a n A)(1+t a n B)=2 (cotA-1)(cot...

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  14. Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-c...

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  15. If tan(alpha+theta)=ntan(alpha-theta) , show that (n+1)sin2theta=(n-1...

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  16. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

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  17. If tan( pi cos theta) = cot ( pi sin theta) then sin (theta + pi/4) e...

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  18. Find the values of the following: sin75^0 (ii) cos75^0 (iii) sin15^0...

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  19. If cotalpha=1/2,secbeta=-5/3,where piltalphalt(3pi)/2and pi/2 ltbetalt...

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  20. If sin A=3/5,0<A<pi/2a n dcosB=(-12)/(13),0<B<(3pi)/2, find the follow...

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