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Prove that (i) "cos " ((pi)/(3) +x)...

Prove that
`(i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x)`
`(ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x`
`(iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) "`
`(iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0`

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RS AGGARWAL-TRIGONOMETRIC , OR CIRCULAR, FUNCTIONS-Exercise (15B)
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  2. Find the values of all trigonometric functions of 135^(@)

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  3. Prove that (i) " sin " 80^(@) "cos " 20^(@) - " cos " 80^(@) ...

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  4. Prove that (i) " sin " (50^(@) + theta ) " cos " (20^(@) + theta)...

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  5. Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin...

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  6. Prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2

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  7. Prove that (i) " sin " 75^(@) =((sqrt(6)+sqrt(2)))/(4)(ii) (cos 13...

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  8. Prove that (i) "cos " 15^(@) - " sin " 15^(@) = (1)/(sqrt(2)) ...

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  9. Prove that (cos 9^(@)+ sin 9^(@))/(cos 9^(@) -sin 9^(@)) = tan 54^...

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  10. Prove that (cos 8^(@) - sin 8^(@))/(cos 8^(@) + sin 8^(@)) = tan 3...

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  11. Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta...

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  12. (cos (pi + theta))/(sin(90^(@) +theta)) +(sin (-theta))/(sin(180^(@) +...

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  13. Prove that: (s in(180^0+theta)cos(90^0+theta)t a n(270^0-theta)cot(360...

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  14. If theta and phi lie in the first quadrant such that sin theta...

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  15. If x and y are acute angles such that sin x =1/sqrt5 and sin y =1/sqrt...

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  16. If x and y are acute angles such that cosx=13/14 and cosy=1/7 , prove...

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  17. If sin x=(12)/(13) "and sin " y= (4)/(5) " where " (pi)/(2) lt ...

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  18. if cos x=(3)/(5) " and cos " y=(-24)/(25) " where " .(3pi)/(2) lt...

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  19. Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt...

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  20. Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (i...

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