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Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5...

Prove that: `sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8`

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Let us consider the LHS

`sin^2 24° – sin^2 6° `

As we know,

`sin (A + B) sin (A – B) = sin^2A – sin^2B `

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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that ; 4 sin 27^@=(5+sqrt(5))-sqrt((3-sqrt(5))) we have

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  2. Prove that : sin^2(72^@) - sin^2 (60^@) = (sqrt5 - 1)/8

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  3. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

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  4. Prove that: sin^2 42^0-cos^2 78^0=(sqrt(5)+1)/8

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  5. Prove that: cos 78^0cos 42^0cos 36^0=1/8

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  6. cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi...

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  7. Prove that cos6^@ . cos42^@. cos66^@ cos78^@= 1/16

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  8. Prove that: sin6^0sin42^0sin 66^0sin 78^0=1/(16)

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  9. Prove that: sin36^0s in 72^0s in 108^0s in 144^0=5/(16)dot

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  10. If cos4x=1+ksin^2x cos^2x , then write the value of kdot

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  11. If tanx/2=m/n ,\ then writhe the value f msinx+n\ cos xdot

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  12. If pi/2<theta<(3pi)/2\ then write the value of sqrt((1+cos2theta)/2)

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  13. If pi/2<theta<pi, then write the value of sqrt(2+sqrt(2+2cos2theta)) i...

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  14. If pi/2<theta<pi , then write the value of sqrt((1-cos2theta)/(1+cos2t...

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  15. If pi<theta<(3pi)/2 , then write the value of sqrt((1-cos2theta)/(1+co...

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  16. Write the value of cos^2 76^@+cos^2 16^@- cos76^@ cos16^@

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  17. If pi/4<theta<pi/2, then write the value of sqrt(1-s in2theta)

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  18. Prove that: cospi/7cos(2pi)/7cos(4pi)/7=-1/8,

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  19. If sin x+cos x=a , find the value of sin^6x+cos^6xdot

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  20. If s in x+cos x=a , find the value of |s in x-cos x|dot

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