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Prove that:(tan 60-tan 30)/(1+tan 60 tan...

Prove that:`(tan 60-tan 30)/(1+tan 60 tan 30)=tan 30`

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KALYANI PUBLICATION-TRIGONOMETRIC RATIOS OF CERTAIN ANGLES-EXERCISE
  1. Evaluate:(cot 60)^2+(sin 30)^2-(cos 90)^2

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  2. Evaluate:(cot 30)^2-2(sin 30)^2-3/4(cosec 45)^2

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  3. Evaluate:(sin 30+tan 45-cosec 60)/(sec 30+cos 60+cot 45)

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  4. Evaluate:(cos 30+sin 60)/(1+cos 30+sin 60)

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  5. Evaluate:((sin 30)^2+(cos 45)^2-4(sin 30)^2)/(2sin 30 cos 30+tan 45)

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  6. Evaluate:((tan 60)^2+4(sin 45)^2+3(sec 30)^2+5(cos 90)^2)/(cos 30 +sin...

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  7. Verify:a.Sin60^@=(2tan30^@)/(1+tan^2 30^@)

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  8. Prove that:cos 60=(1-(tan 30)^2)/(1+(tan 30)^2)

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  9. Prove that:(tan 60-tan 30)/(1+tan 60 tan 30)=tan 30

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  10. Prove that:((1+cot 60)/(1-cot 60))^2=(1+cos 30)/(1-cos 30)

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  11. Prove that:((sin 0+sin 60)(cos 60+tan 45)/(tan 30+cot 60)(cosec 30-cos...

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  12. Prove that:((1+2sin 60cos 60)/(sin 60+cos 60))+((1-2sin 60cos 60)/(sin...

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  13. Prove that:(sec 30)^2-(2tan 30 cosec 60)/(1+(tan 30)^2)-(cot 30)^2=0

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  14. If A=60⁰ and B=30⁰ , verify that sin (A+B)=sin Acos B+cos A sin B

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  15. If A=60⁰ and B=30⁰ , verify that sin (A-B)=sin A cos B-cos A sin B

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  16. If A=60⁰ and B=30⁰ , verify that cos(A+B)=cos A cos B-sin A sin B

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  17. If A=60⁰ and B=30⁰ , verify that cos (A-B)=cos A cos B+sin A sin B

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  18. If A=60⁰ and B=30⁰ , verify that tan (A+B)=(tan A+tan B)/(1-tan A tan ...

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  19. If A=60⁰ and B=30⁰ , verify that tan (A-B)=(tan A-tan B)/(1+tan A tan ...

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  20. If A=60⁰ and B=30⁰ , verify that sin(A+B) sin (A-B)=(sin A)^2-(sin B)^...

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