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Prove that : sin60^(@)=2sin30^(@)cos3...

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

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

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

Verify that : sin 60^@ = 2 sin 30^@ cos 30^@

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

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

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

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

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

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

Prove that: (cos(60^(@)-A)+sin(30^(@)-A))/(cos(30^(@)-A)-sin(60^(@)-A))= cotA

ICSE-TRIGONOMETRICAL RATIOS OF STANDARD ANGLES-EXERCISE 23(A)
  1. Prove that : tan(2 times 30^(@))=(2tan30^(@))/(1-tan^(2)30^(@))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the value of : sin30^(@)cos30^(@)

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  19. Find the value of : tan30^(@)tan60^(@)

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  20. Find the value of : cos^(2)60^(@)+sin^(2)30^(@)

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