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

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

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

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

Prove that: cos(45^(@)+A) cos(45^(@)-A)=1/2 cos2A

Prove that: sec(45^(@)+A)sec(45^(@)-A)=2sec2A

Prove that: "cosec"(270^(@)-A)"cosec"(270^(@)+A)+cot(270^(@)-A)cot(270^(@)+A)=1

Prove that : cot^(2) A - cot^(2) B = (cos^(2) A - cos^(2) B)/ (sin^(2) A sin^(2) B) = cosec^(2) A - cosec^(2)B

Prove that : (1 + cot A)^(2) + (1 - cot A)^(2) = 2 cosec^(2) A

Prove that : sqrt (sec^(2) A + cosec^(2) A) = tan A + cot A

Prove that: 2sec^(2)A-sec^(4)A-2"cosec"^(2)A+"cosec"^(4)A=cot^(4)A-tan^(4)A

Prove that sec 30^(@)tan 60^(@)+sin 45^(@)" cosec "45^(@)+cos30^(@)cot 60^(@)=(7)/(2) .

ICSE-TRIGONOMETRICAL RATIOS OF STANDARD ANGLES-EXERCISE 23(A)
  1. Prove that : sin60^(@)cos30^(@)+cos60^(@).sin30^(@)=1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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