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Prove that 3/4 le cos^2 theta +sin^4 the...

Prove that `3/4 le cos^2 theta +sin^4 thetale1`. Hence deduce that `3/4 le sin^2 theta + cos^4 thetale1`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If A=sin^(2)x+cos^(4)x, then for all real x

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  2. The possible values of theta in (0,pi) such that sin (theta)+sin(4 th...

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  3. Prove that 3/4 le cos^2 theta +sin^4 thetale1. Hence deduce that 3/4 l...

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  4. Prove that : (2 cos 2^n theta +1)/(2cos theta +1)= (2cos theta-1)(2cos...

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  5. Prove that tan alpha+2tan 2 alpha+4 tan 4 alpha+ 8 cos 8 alpha=cot a...

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  6. Solve: 2 (cos x + cos 2x) + sin 2x (1 + 2 cos (x))=2 sinx,-pi le x le ...

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  7. Find the values of x in (-pi, pi), which satisfy the equation : 8^(1+|...

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  8. If p tan theta = tan p theta, then show that : (sin^2 p theta)/(sin^2 ...

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  9. If a+b+c=0, then what is the value of a^2/(bc)+b^2/(ca)+c^2/(ab)

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  10. Given the product p of sines of the angles of a triangle and the produ...

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  11. In a triangle ABC, if (sinA)/(sinC)=(sin(A-B))/(sin(B-C)). Prove that...

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  12. If (tan 3A)/(tan A)=k, show that ( sin 3A)/(sin A)= (2k)/(k-1) and he...

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  13. Prove that : (tan 5 theta+tan3 theta)/(tan 5 theta- tan3 theta)= 4 c...

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  14. Prove that : sin x sin y sin (x - y) + sin y sin z sin (y- z)+ sin z ...

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  15. Solve the equation : sin theta+sin 3 theta+ sin 5 theta =0.

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  16. Solve : sec theta-cosec theta =4/3.

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  17. Solve : 5 sin x cos y = 1, 4 tan x = tan y.

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  18. If A,B,C are the angles of a triangle and sin^3 theta= sin (A- theta)s...

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  19. If the sides a, b, c of a triangle are in A.P., then find the value of...

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  20. Two sides of a triangle are of lengths sqrt6 and 4 and the angle oppos...

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