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Prove that : sin frac (pi)(5) sin frac...

Prove that :
`sin frac (pi)(5) sin frac (2pi)(5) sin frac (3pi)(5) sin frac (4pi)(5) =5/16`.

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Prove that sin frac (pi)(14) sin frac (3 pi)(14) sin frac (5pi)(14) sin frac (7pi)(14)=1/8 .

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Prove that : sin^2 frac (pi)(8)+ sin^2 frac (3pi)(8)+ sin^2 frac (5pi)(8)+sin^2 frac (7pi)(8)=2 .

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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) .

Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=-1/2 .

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

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that : sin frac (pi)(5) sin frac (2pi)(5) sin frac (3pi)(5) si...

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  2. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

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  3. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

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  4. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

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  5. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

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  6. The number of all possible values of theta, where 0 lt theta lt pi, fo...

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

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  8. If sin^ 4 x/2+cos^4 x/3 =1/5 then

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  9. Let theta in (0, pi/4) and t(1)=tan theta)^(tan theta), t(2)=(tan thet...

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  10. if cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [...

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  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

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  12. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

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  13. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

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  14. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

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  15. If A = sin^2x + cos^4 x, then for all real x :

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  16. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

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  17. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

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  18. A triangular park is enclosed on two sides by a fence and on the third...

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  19. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

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