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A DAS GUPTA-Circular Functions, Identities -Exercise
- 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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- If tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4) then prove that sin be...
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- Prove that sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z ...
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- Prove that (3 + cos 4theta) cos 2theta = 4(cos^(8)theta - sin^(8)theta...
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- Prove that cos^(2)theta + cos^(2)(alpha + theta) – 2cos alpha *cos th...
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- If sin beta = 1/5 sin(2alpha +beta), show that tan(alpha +beta) = 3/2...
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- If Tn = sin^(n)theta + cos^(n)theta then prove that (T5 -T3): (T7- T5...
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- If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)bet...
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- If cos A = tan B, cos B = tan C and cos C = tan A then show that sin A...
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- Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ ...
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