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Prove that: t a n 70^0=t a n 20^0+2t a n...

Prove that: `t a n 70^0=t a n 20^0+2t a n 50^0dot`

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To prove that \( \tan 70^\circ = \tan 20^\circ + 2 \tan 50^\circ \), we can follow these steps: ### Step 1: Use the tangent subtraction formula We start with the formula for the tangent of the difference of two angles: \[ \tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b} \] Let \( a = 70^\circ \) and \( b = 20^\circ \). Then we have: ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. Prove that: (cos^2 33^@-cos^2 57^)/(sin(21)^@-cos(21))=-1/sqrt(2)

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  2. Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=co...

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  3. Prove that: t a n 70^0=t a n 20^0+2t a n 50^0dot

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  4. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  5. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  6. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  7. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  8. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  9. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  10. If sinA=12/13 and sinB=4/5 where pi/2 < A < pi and 0 < B < pi/2 then f...

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  11. Prove that sinx/cos(3x)+sin(3x)/cos(9x)+sin(9x)/cos(27x)=1/2 (tan27x-t...

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  12. If s in A=3/5, cos B=-(12)/(13),\ w h e r e A and B both lie in second...

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  13. If cosA=4/5 and cos B=12/13 where and (3pi)/2 < B < A < 2pi then f...

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  14. If cosA=4/5 and cos B=12/13 where (3pi)/2 < B < A < 2pi then find c...

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  15. If tanA=3/4,cosB=9/(41), w h e r e\ pi<A<(3pi)/2a n d\ 0<B<pi/2 , find...

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  16. If sinA=1/2,cosB=(12)/(13), w h e r e pi/2ltaltpia n="" d(3pi)="" 2ltb...

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  17. If sinA=1/2,cosB=(sqrt(3))/2,\ w h e r e\ pi/2<A<pi\ a n d\ 0<B<pi/2 ,...

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  18. If sinA=1/2,cosB=(sqrt(3))/2, w here pi/2 lt A lt pi and 0ltBltpi/2 f...

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  19. Evaluate the following: sin 78^0cos 18^0-cos 78^0sin 18^0

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  20. Evaluate the following: sin 36^0cos9^0+cos36^0 sin9^0

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