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Find the smallest positive values of `xa n dy` satisfying `x-y=pi/4a n dcotx+coty=2`

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ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. Prove that : cosec theta + cosec 2 theta + cosec 2^2 theta +.............

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  2. Find the maximum & minimum values of 27^(cos2x). 81^(s in2x)

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  3. Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...

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  4. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

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  5. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

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  6. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

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  7. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

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  8. If (1+t a n1^0)dot(1+t a n2^0)dot(1+t a n3^0)(1+tan45^0)=2^n , then ' ...

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  9. Prove that in an acute triangle ABC, the least values of Sigma secA an...

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  10. If tan(alpha)= p/q where alpha=6 beta, alpha being an acute angle, pr...

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  11. If tan(pi/4+)=tan^3(pi/4+x/2)dot Prove that (siny)/(sinx)=(3+sin^2x)/...

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

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  13. If P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/19)+....+cos((17pi)/19) and Q=...

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  14. Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

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

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  16. Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3

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  17. If the product (sin1^0)(sin3^0)(sin5^0)(sin7^0)....(sin 89^0)=1/(2^n) ...

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  18. For 0<theta<pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+((m-1)/...

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  19. If (1+sint)(1+cost)=5/4dot Find the value (1-sint)(1-cos t)

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  20. Find the exact value of tan^2(pi/16)+tan^2((3pi)/16) + tan^2((5pi)/16)...

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