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Prove that: tan 35° tan 40° tan 45° ta...

Prove that:
`tan 35° tan 40° tan 45° tan 50° tan 55° = 1`.

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KALYANI PUBLICATION-Complementary Angles and there Trigonamytry Ratios-EXERCISE
  1. Prove that: tan 5° tan 85° tan 30° tan 65° tan 25° = 1/sqrt 3.

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  2. Prove that: tan 4° tan 43° tan 47° tan 86° = 1.

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  3. Prove that: tan 35° tan 40° tan 45° tan 50° tan 55° = 1.

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  4. Prove that: cosec (65° + theta) - sec (25° - theta) - tan (55° - the...

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  5. Prove that: (2 sin 68°)/(cos 22°)-( 2 cot 15°)/( 5 tan 75°)- 3( tan ...

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  6. Prove that: (cos^2 20° + cos^2 70°)/(sin^2 20° + sin^2 70°) +sin^2 6...

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  7. Prove that: (tan 50° + sec 50°)/(cot 40° + cosec 40°) + cos 40° cose...

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  8. In a ∆ ABC prove that sin( (A+B)/2) = COS (c/2).

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  9. In a ∆ ABC prove that cos ((A+B)/2) = sin (c/2).

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  10. In a ∆ ABC prove that tan( (A+B)/2) = cot( C/2).

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  11. In a ∆ ABC prove that sec^2 (B+C)/2 -1=cot^2 A/2.

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  12. If A +B = 90, prove that (cos A + cos B)/(sin A+ sinB)=1.

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  13. If A +B = 90, prove that (tan A + cosec B)^2=(1+sin A)/(1- cos B).

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  14. If A +B = 90, prove that (sin A- sin B)^2 = 1-2 sin A cos A.

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  15. If A +B = 90, prove that cos A = sqrt (cos A/sin B - sin A cos B).

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  16. If A +B = 90, prove that 1+ tan A/tan B + sin^2 A+ sin^2 B = 1+ sec^...

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  17. If sinA =cosB, then show that A+B=90.

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  18. If sintheta +costheta =p and sectheta+cosectheta=q, show that q(p^2 ...

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  19. If sectheta =sqrt(p^2+q^2)/q, then the value of (p sintheta-q costhet...

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  20. Express cos 75° + cot 75° in terms of angle between 0° and 30°.

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