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If A+B=45^(@)," show that "(1+tan A) (1+...

If `A+B=45^(@)," show that "(1+tan A) (1+tan B)=2` and hence deduce the value of `tan"" 22""1^(@)/2`.

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The correct Answer is:
`sqrt2-1`
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FULL MARKS-TRIGONOMETRY-Additional Questions Solved
  1. Prove that (i) sin A+sin (120^(@)+A)+sin(240^(@)+A)=0 (ii) cos A+c...

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  2. If tan A=5/6, tan B=1/11," show that A+B=45"^(@).

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  3. If A+B=45^(@)," show that "(1+tan A) (1+tan B)=2 and hence deduce the ...

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  4. If tanalpha=1/3,tanbeta=1/7,show that 2alpha +beta=pi/4

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  5. If 2 cos theta=x+1/x then prove that cos 2 theta=1/2 (x^(2)+1/x^(2))

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  6. Prove that cos 20^(@) cos 40^(@) cos 80^(@)=1/8

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  7. Show that 4 sin A sin (60^(@)+A). Sin (60^(@)-A) =sin 3A

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  8. Prove that cos 20^(@) cos 40^(@) cos 80^(@)=1/8

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  9. Prove that sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)=3/(16).

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  10. Prove that sin 50^(@)-sin 70^(@)+cos 80^(@)=0.

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  11. Prove that (cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2...

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  12. Prove that 2 cos""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/...

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  13. Prove that (2 cos 2 theta+1)/(2 cos 2theta-1)=tan(60^@+theta) (tan 60^...

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  14. Prove that cos 20^@ cos 40^@ cos 80^(@)=1/8.

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  15. Prove that tan 70^(@)-tan 20^(@)-2 tan 40^(@)=4 tan 10^(@)

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  16. Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

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  17. Prove that (sin 11 A sin A+sin 7A sin 3A)/(cos 11 A sin A+cos 7A sin 3...

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  18. If A + B + C = 180^(@), prove that sin 2A + sin 2B + sin 2C = 4 sin ...

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  19. If A+B+C=pi, " prove that sin"^(2) ""A/2+sin^(2) ""B/2+sin^(2) ""C/2=...

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  20. Solve 2 cos^(2) theta+3 sin theta=0

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