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A DAS GUPTA-Circular Functions, Identities -Exercise
- Prove that 3/4 le sin^(2)theta +cos^(4) theta le 1 for all real theta.
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- Eliminate theta between cosec theta -sin theta = m and sec theta - cos...
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- If cos alpha + cos 2alpha = p,sin alpha + sin 2alpha = q then eliminat...
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- If cos alpha = cos beta*cos phi= cos gamma *cos theta and sin alpha = ...
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- Eliminate theta between a = cos(theta - alpha), b = sin(theta - beta) ...
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- Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha ...
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- If cos rx + cos ry = ar, r = 1, 2, 3 then prove that 2a1^(3) + a3 = 3...
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- Eliminate theta, phi from sin theta + sin phi = a, cos theta+ cos phi ...
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- Eliminatetheta from lambda cos 2theta = cos(theta + alpha) and lambda...
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- If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta). find the ra...
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- Prove that the value of 5 cos theta + 3cos (theta + pi/3) +3 lies bet...
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- If f(theta) = 11cos^(2)theta + 15sin theta cos theta - 9sin^(2)theta, ...
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- Find the maximum and minimum values of sin^(6)x + cos^(6)x.
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- In triangle ABC, B = pi/3 and sin A . sin C = x then find the set of ...
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- Prove that the relation sin^(2)theta = (x+y)^(2)/(4xy) is not possib...
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- Prove that sin theta = x + p/x is possible for real x if p le 1/4
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- If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...
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- If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...
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- If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...
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- If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...
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- Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot thet...
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