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If A+B+C=pi, prove that tan^2A/2+tan^2B/...

If `A+B+C=pi,` prove that `tan^2A/2+tan^2B/2+tan^2C/2geq1.`

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ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  2. Evaluate (2cos4 0^(@)-cos2 0^(@))/(sin2 0^(@)

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  3. Solve cos^6(pi/16)+cos^6((3pi)/16)+cos^6((5pi)/16)+cos^6((7pi)/16)

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  4. Given that (1+tan1^@)(1+tan2^@)...........(1+tan45^@)= 2^n find n .

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  5. Prove that from the equality (sin^(4)alpha)/a+(cos^(4)alpha)/b=1/(a+b)...

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  6. If a leq 3 cos (theta+pi/3)+5cos theta+3 leq b, find a and b, where ...

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  7. The value of (cotθ+cosecθ-1)/ (cotθ-cosecθ+1) is

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  8. If x and y are real number such that x^2 +2xy-y^2=6, find the minimum...

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  9. If A+B+C=pi, prove that tan^2A/2+tan^2B/2+tan^2C/2geq1.

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  10. solve the equation for x , 5^(1/2)+5^(1/2 + log5 sinx) = 15^(1/2 + log...

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  11. Find values of theta satisfying sintheta+sin5theta=sin3theta such that...

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  12. Which of the following are the solutions of equation 2sin 11x + cos3x ...

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  13. Find all value of theta, between 0 & pi, which satisfy the equation;...

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  14. Find the general solution of the equation, 2+tanx.cot(x/2) +cotx.tan(x...

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  15. Determine the smallest positive value of x which satisfy the equation ...

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  16. Find the general solution of the trignometric equation 3^(1/2+log(3)(c...

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  17. Find the value of theta, which satisfy 3-2 cos theta-4 sintheta-cos 2...

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  18. The range of 'y, such that the equation in x, y + cos x = sin x has a ...

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  19. Find the general solution values of theta for which the quadratic (sin...

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  20. Prove that (sec^ 2θ−1)(cosec^ 2θ−1)=1

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