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Prove that: sum(k=1)^(100)sin(k x)cos(10...

Prove that: `sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)`

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ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that: sum(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

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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 t1=(tan theta)^(tan theta), t2=(tan theta)^(...

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

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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. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

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

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