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

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

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

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

Show that : cos^(2)60^(@)-sin^(2)60^(@)=-sin30^(@)

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

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

Evaluate cos45^(@)cos30^(@)+sin45^(@)sin30^(@) .

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

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

Find (in each case, given below) the value of x, if : cos x = cos 60^(@) cos 30^(@) - sin 60^(@) sin 30^(@)

ICSE-TRIGONOMETRICAL RATIOS OF STANDARD ANGLES-EXERCISE 23(A)
  1. Find the value of : 3sin^(2)30^(@)+2tan^(2)60^(@)-5cos^(2)45^(@)

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

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

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  4. Prove that : cosec^(2)45^(@)-cot^(2)45^(@)=1

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

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  6. Prove that : ((tan60^(@)+1)/(tan60^(@)-1))^(2)=(1+cos30^(@))/(1-cos3...

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  7. Prove that : 3cosec^(2)60^(@)-2cot^(2)30^(@)+sec^(2)45^(@)=0.

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

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

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

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

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

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

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

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

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

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

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

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

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

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