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Find the value of sin^(2)42^(@)-sin^(2)1...

Find the value of `sin^(2)42^(@)-sin^(2)12^(@)`.

A

`(sqrt(5)-1)/(4)`

B

`(sqrt(5)+1)/(4)`

C

`(sqrt(5)-1)/(8)`

D

`(sqrt(5)+1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 C ( MULTIPLE AND SUBMULTIPLE ANGLES )
  1. Evaluate 6 sin 20^(@) - 8 sin^(3)20^(@).

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  2. tan 9^(@) - tan 27^(@) - tan 63^(@) + tan 81^(@) =

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  3. Find the value of sin^(2)42^(@)-sin^(2)12^(@).

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  4. Find the value of cos^(2)72^(@) - sin^(2) 54^(@).

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  5. 8 cos^(3) 10^(@) -6 cos 10^(@) =

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  6. 8 cos^(3) 20^(@) -6 cos 20^(@) =

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  7. 4(cos^3 20^(@) + cos^(3) 40^(@))=

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  8. 4( cos^(3) 10^(@) + sin^(3) 20^(@))=

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  9. if ( cos ^(3) 20^@ + cos^(3) 40^(@))/( cos 20^@+ cos 40^(@)) = k ,the...

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  10. cos theta cos (60^(@) + theta ) * cos (60^(@) - theta ) =

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  11. sin^(2) theta + sin^(2)(60^@ + theta ) + sin^(2)(60^(@) - theta ) =

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  12. cos^(2) A + cos^(2) ( 120^(@) + A)+ cos^(2) (120^(@) - A )=

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  13. cos^(3) theta + cos^(3) ( 120^(@) +theta ) + cos^(3) (120^(@) - theta ...

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  14. sin^(2) 20^(@) + sin^(2) 100^@ + sin^(2) 140^(@) =

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  15. cos^(3) 20^(@) + cos^(3) 100^(@) + cos^(3) 140^(@) =

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  16. cos^(2)(theta-45^(@))+cos^(2)(theta+15^(@)-cos^(2)(theta-15^(@))=

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  17. If 4 sin(60^(@) + theta ) sin (60^(@) - theta )-1=k cos 2 theta , th...

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  18. Show that sin ^(4). (pi)/(8)+ sin ^(4) .(3pi)/(8) sin ^(4). (5pi)/(8)...

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  19. Show that cos^4""pi/8+cos^4""(3pi)/8+cos^4""(5pi)/8+cos^4""(7pi)/8=3/2

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  20. tan ""7(1^@)/(2)=

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