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

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

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The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

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ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) fo...

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

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

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  4. If A +B+C=pi, prove that tan^(2)""(A)/(2)+tan^(2)""(B)/(2)+tan^(2)""(C...

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  5. If alpha+beta+gamma=pi, prove that : cos^2 alpha + cos^2 beta + cos^2 ...

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  6. In a DeltaABC, if cot A+cot B+cot C=sqrt3. Prove that the triangle is ...

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

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  8. For 0ltthetalt pi/2 the solutions(s) of sum(m=1)^6 cosec (theta+ ((m-1...

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  9. If (1+sint)(1+cot t)=(5)/(4) then find the value of (1-sint)(1-cos t).

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  10. tan^(2)'(pi)/(16)+tan^(2)'(2pi)/(16)+tan^(2)'(3pi)/(16)+tan^(2)'(5pi)/...

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  11. Let x1=prod(r=1)^5cos(rpi)/(11)\ a n d\ x2=sum(r=1)^2cos(rpi)/(11), th...

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  12. The period of the function f(x)=sin^(4)x+cos^(4)x is:

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  13. If y=sec^2theta+cos^2theta,\ theta!=0, then- a.y=0 b. ylt=2 c. ygeq-2 ...

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  14. The value of (1-tan^215^0)/(1+tan^215^0)= (A) 1 (B) sqrt(3) (C) sqrt(3...

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  15. If alpha is a root of 25 cos^2theta+5costheta-12=0, pi/2 < alpha < pi,...

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  16. If sin(alpha+beta)=1, sin(alpha-beta)=1/2 then, tan(alpha+2beta) tan(2...

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  17. If tantheta=-4/3,t h e nsintheta is -4/5b u tnot4/5 (b) -4/5or4/5 ...

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  18. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if (a)x+y!=0 (b)...

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  19. If u=sqrt(a^2 cos^2 theta + b^2sin^2theta)+sqrt(a^2 sin^2 theta + b^2 ...

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  20. Let alpha and beta be such that pi<alpha-beta<3pi, If sinalpha+sinbeta...

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