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A DAS GUPTA-Circular Functions, Identities -Exercise
- Show that there is no real x for which e^(sin x) - e^(-sin x) = 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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- Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x *cos 2x *cos 3x.
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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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- 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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- If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a ...
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- If sin theta - sin phi = a and cos theta + cos phi = b then prove tha...
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- If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove...
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- If sin alpha + sin beta =p, cos alpha + cos beta = q then find the va...
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- If cos(x - y)= -1, show that cos x + cos y = 0 and sin x + sin y = 0.
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