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Prove that (cos alpha+cos beta)^(2)+(sin...

Prove that `(cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2) ((alpha+beta)/(2))`

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The correct Answer is:
`4 cos^(@) ((alpha+beta)/(2))`
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FULL MARKS-TRIGONOMETRY-Additional Questions Solved
  1. Prove that sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)=3/(16).

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

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

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

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

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

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

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

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

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

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

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

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  13. Solve: 2 tan theta-cot theta=-1

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  14. Solve tan^(2) theta+(1-sqrt3) tan theta-sqrt3=0

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  15. Solve sqrt3 sin x+cos x=2

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  16. Solve sin^(2) theta-2 cos theta+1/4=0

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  17. In any triangle prove that a^2 =(b+c)^2 sin^2 (A/2) +(b-c)^2 cos^2 (A/...

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  18. Show that cosA/a +cosB/b +cosC/c =(a^2 +b^2 +c^2 )/2abc

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  19. Prove that (sin (A-B))/(sin (A+B))=(a^(2)-b^(2))/(c^(2))

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  20. Show that cos[(B-C)/2]=(b+c)/a sin(A/2)

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