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Prove that: tan10^0tan15^0tan75^0tan80^0...

Prove that: `tan10^0tan15^0tan75^0tan80^0=1` `tan1^0tan2^0tan3^0.....tan89^0=1` `cos1^0cos2^0cos3^0.......cos180^0=0`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS-All Questions
  1. If sin(A+B)=1 and cos(A-B)=(sqrt(3))/2, then find A and B dot

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  2. Evaluate each of the following: cot 12^circcot 38^circcot52^circcot60^...

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  3. Prove that: tan10^0tan15^0tan75^0tan80^0=1 tan1^0tan2^0tan3^0.....tan...

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  4. If A+B=90^0, prove that sqrt((tanAtanB+tanAcotB)/(sinAsecB)-(sin^2B)/(...

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  5. If sin5theta=cos4theta, whre 5thetaa n d4theta are acute angles, find ...

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  6. If tantheta+1/(tantheta)=2 , find the value of tan^2theta+1/(tan^2thet...

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  7. Evaluate each of the following in the simplest form: 1).cosec30^0+cot...

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  8. In a right triangle ABC , right angled at B , the ratio of A BtoA C is...

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  9. In Figure, A D=D B \ and \ /B is a right angle. Determine. (a)\ sin th...

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  10. Find the value of x in each of the following: (i)tan3x=sin45^0cos45^...

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  11. If theta is an acute angle and tantheta+cottheta=2, find the value o...

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  12. Prove that: (cos30^0+sin60^0)/(1+cos60^0+sin30^0)=(sqrt(3))/2

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  13. Find the value of theta in each of the following: (i)2sin2theta=sqrt...

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  14. An equilateral triangle is inscribed in a circle of radius 6cm. Find ...

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  15. If tanA=1 and tanB=sqrt(3),e v a l u a t ecosAcosB-sinAsinBdot

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  16. Evaluate each of the following: cos(40^0-theta)-sin(50^0+theta)+(cos^2...

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  17. If s e c4A=cos e c(A-20^@) , where 4A is an acute angle, find the ...

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  18. Evaluate each of the following: (a) cos(40^0-theta)-sin(50^0+theta)...

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  19. Evaluate : 4(sin^4 30^0+cos^4 60^0)-2/3(sin^2 60^0-cos^2 45^0)+1/2tan...

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  20. Evaluate : (sin50^0)/(cos40^0)+(cos e c40^0)/(sec50^0)-4cos50^0cos e ...

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