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Evaluate the following: sin 78^@ cos 18^...

Evaluate the following: `sin 78^@ cos 18^@-cos 78^@ sin 18^@`

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To evaluate the expression \( \sin 78^\circ \cos 18^\circ - \cos 78^\circ \sin 18^\circ \), we can use the sine subtraction formula. ### Step-by-Step Solution: 1. **Identify the Formula**: We recognize that the expression resembles the sine subtraction formula: \[ \sin(a - b) = \sin a \cos b - \cos a \sin b \] ...
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MAHAVEER PUBLICATION-TRIGONOMETRIC RATIOS-QUESTION BANK
  1. If tan (A+B)=p, tan(A-B)=q find tan 2A.

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  2. If tantheta=a/b , show that (asintheta-bcostheta)/(asintheta+bcostheta...

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  3. Evaluate the following: sin 78^@ cos 18^@-cos 78^@ sin 18^@

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  4. Evaluate the following: cos 47^@ cos 13^@-sin 47^@ sin 13^@

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  5. Find the value of the following trigonometric functions: sin 765^@

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  6. Find the value of the following trigonometric functions:cos(-1410^@)

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  7. Find the value of the following trigonometric functions:sin(-(11pi)/3)

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  8. Find the value of the following trigonometric functions:cot(-(15pi)/4)

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  9. Find the value of the following trigonometric functions:cos(-(31pi)/3)

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  10. Find the value of the following trigonometric functions:sin 570^@

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  11. Find the value of the following trigonometric functions:tan(-1125^@)

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  12. Find the value of the following trigonometric functions:sin 1110^@

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  13. Find the value of the following trigonometric functions:sin 660^@

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  14. Find the value of the following trigonometric functions: cos(-225^@)

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  15. Show that sin^2 20^@+sin^2 70^@=1

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  16. Show that sin^2 49^@+sin^2 41^@=1

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  17. Show that sin^2 36^@+sin^2 54^@=1

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  18. Show that sin^2 46^@+sin^2 44^@=1.

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  19. Prove that sqrt((1+sintheta)/(1-sintheta))+sqrt((1-sintheta)/(1+sinthe...

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  20. Prove thatsqrt((cosec theta+cottheta)/(cosec theta-cottheta))=(sin the...

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