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Prove that : 1+tan A tan frac (A)(2)= ...

Prove that :
`1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1`

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If A + B + C =180^@ , prove that : tan frac (A)(2) tan frac (B)(2)+ tan frac (B)(2) tan frac (C)(2) +tan frac (C)(2) tan frac (A)(2)=1 .

Prove that : (sinx)/(1+cos x)= tan frac (x)(2) .

Prove that: (tanA+secA-1)/(tan A -secA +1)= secA+tanA .

In a triangle ABC, tan frac (A)(2)=5/6, tan frac (C)(2)=2/5 , then :

If A + B + C =180^@ , prove that : cot frac (A)(2)+cot frac (B)(2)+cot frac (C)(2)= cot frac (A)(2) cot frac (B)(2) cot frac (C)(2) .

Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) cot frac(pi)(4)=1 .

If A + B + C =180^@ , prove that : sin^2 frac (A)(2)+ sin^2 frac (B)(2)+sin^2 frac (C)(2)=1-2 sin frac (A)(2)sin frac (B)(2)sin frac (C)(2) .

If A + B + C =180^@ , prove that : sin^2 frac (A)(2)+ sin^2 frac (B)(2)-sin^2 frac (C)(2)=1-2 cos frac (A)(2)cos frac (B)(2)sin frac (C)(2) .

In any triangle ABC, prove that : sin frac (A)(2) +sin frac (B)(2)+sin frac (C)(2)=1+4 sin frac (pi-A)(4) sin frac (pi-B)(4) sin frac (pi-C)(4) .

If the sides a, b, c of a triangle are in A.P., then find the value of tan frac (A)(2)+ tan frac (C)(2) in terms of cot frac (B)(2) .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : tan 13A-tan 9A- tan 4A= tan 13A tan 9A tan 4A.

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  2. If cos (alpha+beta) sin (gamma+delta)=cos (alpha-beta) sin (gamma-delt...

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  3. Prove that : 1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1

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  4. If cot alpha cot beta=2, show that (cos (alpha+beta))/(cos (alpha-beta...

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  5. Prove that : tan 50^@ = tan 40^@ + 2 tan 10^@ .

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  6. Prove that : 2 tan 70^@ = tan 80^@ - tan 10^@.

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  7. If cos A=5/13 and sin B= 4/5 , find sin (A + B), where A, B, (A + B) ...

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  8. If tan x= a/(a+1) and tan y=1/(2a+1), show that one of the values of :...

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  9. In any quadrilateral ABCD, show that : cos A cos B - cos C cos D = si...

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  10. Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4).

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  11. Prove that : tan (x-y)+tan (y -z) + tan (z-x)= tan (x-y)tan (y -z) t...

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  12. Prove that : cos^2 (pi/8+x/2)-sin^2 (pi/8-x/2)= 1/sqrt2 cos x.

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  13. Prove that : (cos^2 33^@- cos^2 57^@)/(sin^2 frac (21^@) (2)- sin^2 fr...

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  14. Find a and b such that a le3 cos theta +5 sin (theta-pi/6)le b holds ...

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  15. If sin alpha=15/17 and cos beta=12/13, find the values of : sin (alpha...

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  16. If sin alpha=15/17 and cos beta=12/13, find the values of : cos (alph...

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  17. If sin alpha=15/17 and cos beta=12/13, find the values of : tan (alph...

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  18. If cos (alpha+beta)=4/5, sin (alpha -beta)=5/13 and alpha, beta lie b...

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  19. Find the value of tan (alpha+beta), given that : cot alpha=1/2, alpha...

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  20. If theta+phi= alpha and tan theta=k tan phi, prove that : sin alpha=(...

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