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For all theta in [0,pi/2] show that cos(...

For all `theta` in `[0,pi/2]` show that `cos(sintheta)gtsin(costheta)`

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For 0ltxltpi/ 2, prove that cos(sinx)gtsin(cosx)

If cos theta -sin theta =sqrt(2) sin theta , show that, costheta+sintheta=sqrt(2) cos theta [0ltthetaltpi/2] .

For real values of theta, which of the following is/are always positive? "cos"(costheta) (b) cos(sintheta) sin(costheta) (d) sin(sintheta)

Prove that for all values of theta , |{:(sintheta,costheta,sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2pi)/(3)),sin(2theta+(4pi)/(3))),(sin(theta-(2pi)/(3)),cos(theta-(2pi)/(3)),sin(2theta-(4pi)/(3))):}|=0

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

If 3sintheta+4costheta=5, then show that 4sintheta-3costheta=0.

If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

If costheta= x/sqrt(x^2+y^2) show that x sin theta = y cos theta .

Solve : 2cos^2theta+3sintheta=0

Solve the equation 2cos^2theta+3sintheta=0

PATHFINDER-TRIGONOMETRIC RATIOS AND IDENTITIES-QUESTION BANK
  1. In a Delta ABC

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  2. If the circumcentre of DeltaABC lies on incircle then cosA+cosB+cosC=s...

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  3. For all theta in [0,pi/2] show that cos(sintheta)gtsin(costheta)

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  4. Show that the value of the function (sinxcos3x)/(cosxsin3x), where eve...

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  5. if alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2co...

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  6. If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 prove that cos(alpha-...

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  7. Find the value of t, where t in [-pi/2,pi/2] so that 2sint=(5x^2-2x+1...

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  8. If exp{(sin^2 x+sin^4 x+sin^6 x+...)In2} satisfies the quadratic equat...

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  9. If A+B+C=180^@ prove that: sin(B+2C)+sin(C+2A)+sin(A+2B)= 4 sin((B-C)/...

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  10. Prove that (1+sec2theta)(1+sec2^2theta)(1+sec2^3theta)…..(1+sec2^nthet...

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  11. If cot(2x/3)+tan(x/3)=cosec(kx)/3 then the value of k is

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  12. যদি thetain(frac[pi][2],frac[3pi][2]) হয়, তবে sqrt(4cos^4theta+sin^2(2...

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  13. Which one of the following statements is correct ?

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  14. For x belongs to (o,pi) the equation sinx+2sin2x-sin3x=3 has

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  15. Let fk(x)=1/k(sin^k x+cos^k x) Then f4(x)-f6(x) =

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  16. The value of tan(pi/3)+2tan((2pi)/3)+4cot((4pi)/3)+8tan((8pi)/3) is

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  17. The sum of the series underset(n=1)sum sin((nipi)/720) is

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  18. The minimum value of 2^(sin x) + 2^(cos x) is

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  19. cos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)

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

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