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Prove that : 4(sin^(4)30^(@)+cos^(4)6...

Prove that :
`4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2`

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Prove that : (i) sin 60^(@) = 2 sin 30^(@) cos 30^(@) (ii) 4(sin^(4) 30^(@) + cos^(4) 60^(@)) - 3(cos^(2)45 - sin^(2)90^(@)) = 2

Prove that : sin60^(@)=2sin30^(@)cos30^(@) .

Prove that : sin60^(@)=2sin30^(@)cos30^(@) .

Prove that : cos^(2)30^(@)-sin^(2)30^(@)=cos60^(@)

Prove that : cos^(2)30^(@)-sin^(2)30^(@)=cos60^(@)

Prove that : sin60^(@)cos30^(@)+cos60^(@).sin30^(@)=1

Find the value of : 3sin^(2)30^(@)+2tan^(2)60^(@)-5cos^(2)45^(@)

Find the value of : 3sin^(2)30^(@)+2tan^(2)60^(@)-5cos^(2)45^(@)

i) Prove that: cos^(3)2A+3cos2A = 4(cos^(6)A-sin^(6)A) ii) Prove that: 4(cos^(3)10^(@) + sin^(3)20^(@)) = 3(cos10^(@)+sin20^(@))

Prove that : cos30^(@).cos60^(@)-sin30^(@).sin60^(@)=0

ICSE-TRIGONOMETRICAL RATIOS OF STANDARD ANGLES-EXERCISE 23(A)
  1. Prove that : 3cosec^(2)60^(@)-2cot^(2)30^(@)+sec^(2)45^(@)=0.

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  2. Prove that : sin(2 times 30^(@))=(2tan30^(@))/(1+tan^(2)30^(@))

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  3. Prove that : cos(2 times 30^(@))=(1-tan^(2)30^(@))/(1+tan^(2)30^(@))

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  4. Prove that : tan(2 times 30^(@))=(2tan30^(@))/(1-tan^(2)30^(@))

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  5. ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find ...

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  6. Prove that : sin60^(@)=2sin30^(@)cos30^(@).

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  7. Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)...

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  8. If sinx =cosx and x is acute, state the value of x.

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  9. If secA=cosecA" and "0^(@) le A le 90^(@), state the value of A.

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  10. If tantheta=cottheta" and "0^(@) le theta le 90^(@), state the value o...

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  11. If sinx=cosy, write the relation between x and y, if both the angles x...

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  12. If sinx=cosy, then x+y=45^(@), write true or false.

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  13. sectheta.cottheta=cosectheta, write true or false.

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  14. For any angle theta, state the value of : " "sin^(2)theta+cos...

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  15. State for any acute angle theta whether : sintheta increases or decr...

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  16. State for any acute angle theta whether : costheta increases or decr...

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  17. State for any acute angle theta whether : tantheta increases or decr...

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  18. If sqrt(3)=1*732, find (correct to two decimal places) the value of ea...

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  19. Evaluate : (cos3A-3cos4A)/(sin3A+2sin4A)," when "A=15^(@).

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  20. Evaluate : (3sin3B+2cos(2B+5^(@)))/(2cos3B-sin(2B-10^(@))), when B...

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