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Find acute angles A and B if sin (A+ 2B)...

Find acute angles A and B if sin (A+ 2B) =`(sqrt3)/2` and `cos (A+ 4B) = 0, A gt B, 0° ltA+ 2B le90°, 0° ltA+ 4B le90°`.

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The correct Answer is:
`A=30^(@),B=15^(@)`
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KUMAR PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Test Your Skills
  1. Find x if sqrt3 tan 2x = cos 60° + sin 45° cos 45°

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  2. If A= 30° and B = 60°, verify that cos (A+ B) = cos A cos B - sin A si...

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  3. Find acute angles A and B if sin (A+ 2B) =(sqrt3)/2 and cos (A+ 4B) = ...

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  4. If A and B are acute angles such that tanA=1/2,tanB=1/3 and tan(A+B)=(...

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  5. Evaluate the following : (tan35^(@))/(cot55^(@))+(cot78^(@))/(tan12^...

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  6. Evaluate the following : (sin72^(@)+cos18^(@))(sin72^(@)-cos18^(@))

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  7. Evaluate the following : sec50^(@)sin40^(@)+cos40^(@)cosec50^(@)

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  8. Express each of the following in terms of trigonometric ratios of ang...

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  9. Express each of the following in terms of trigonometric ratios of ang...

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  10. Express each of the following in terms of trigonometric ratios of ang...

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  11. Prove that : tan 20° tan 35° tan 45° tan 55° tan 70° = 1

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  12. Prove that : (cos80^(@))/(sin10^(@))+cos59^(@)cosec31^(@)=2

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  13. If sin theta = cos (theta-45°), where theta and theta- 45° are acute a...

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  14. Evaluate : ( 1 ) cosec (65° +theta) -sec (25° - theta) - tan (55° + ...

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  15. Express all the other trigonometric ratios of angleA in terms of sin ...

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  16. If sintheta=1/3 find the value of 2cot^(2)theta+2.

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  17. Evaluate : 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)...

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  18. Prove the following identities : sec^(2)theta-cos^(2)theta=sin^(2)th...

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  19. Prove the following identities : ((1+tan^(2)A)cotA)/(cosec^(2)A)=tan...

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  20. Prove the following identities : 1/( sectheta-tantheta)-1/(costheta)...

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