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Find sin x/2 ,cos x/2 and t a n x/2 of t...

Find `sin` `x/2` `,cos` `x/2` and `t a n` `x/2` of the following : `s in" "x" "=1/4,` x in quadrant II.

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The correct Answer is:
(i) `(2)/(sqrt5),(1)/(sqrt5),2`
(ii) `sqrt((2)/(3)),-sqrt((1)/(3)),-sqrt2`
(iii) `(sqrt(8+2sqrt(15)))/(4),(sqrt(8-2sqrt(15)))/(4),4+sqrt(15)`.
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MODERN PUBLICATION-TRIGONOMETRY-Exercise 3(g)Long Answer type Question-I
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  2. If cos theta=(1)/(2)(alpha+(1)/(alpha)),prove that: (i) 2 cos 2thet...

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  3. If x+(1)/(x)=2costheta, then find the valueof x^(3)+(1)/(x^(3)).

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  4. Prove that: (i) cos A cos(60^(@)-A)cos (60^(@)+A)=(1)/(4)cos 3A ...

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  5. cos^2alpha+cos^2(alpha+120^0)+cos^2(alpha-120^0)=3/2

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  6. If tan^2theta=1+2tan^2phi then show that cos2theta+sin^2phi=0

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  7. Find sin x/2 ,cos x/2 and t a n x/2 of the following : s in" "x" "=1/...

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  8. (i) If "tan""(x)/(2)=(m)/(n),prove that m sin x+n cos x=n. (ii) If...

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  9. Prove that (cos^(3)theta-cos 3theta)/(cos theta)+("sin"^(3)theta+"sin"...

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  10. Evaluate: (i) "sin""(3pi)/(8) (ii) "sin""(5pi)/(24) (iii) "tan""(pi...

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  11. Prove that: s in^4pi/8+s in^4(3pi)/8+s in^4(5pi)/8+s in^4(7pi)/8=3/2

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  12. Prove that: (i) "sin"^(2)6x-"sin"^(2)4x="sin" 2x sin 10x (ii) c...

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  13. Find "sin" 7(1^(@))/(2),cos 7(1^(@))/(2) and "tan" 11(1^(@))/(4).

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  14. Prove that: "tan" 142(1^(@))/(2)=2+sqrt2-sqrt3-sqrt6.

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  15. Prove that cotxcot2x-cot2xcot3x-cot3xcotx=1

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  16. Prove that: (i) sin 3x+"sin" 2x-"sin" x =4 sin x cos((x)/(2))cos...

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  17. Prove that cos^2x+cos^2(x+pi/3)+cos^2(x-pi/3)=3/2

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  18. If cos theta=(cos phi-e)/(1-e cos phi),show that: "tan"(theta)/(2)...

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