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A DAS GUPTA-Circular Functions, Identities -Exercise
- Find the set of possible values of (tan(x + pi/6))/tan x where x is an...
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- Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...
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- Show that (sec^(2)theta - tan theta)/(sec^(2)+ tan theta) lies betwe...
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- Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...
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- Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-...
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- Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...
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- Prove that sum(r=1)^(10) = sin^(2) rpi/18 =5.
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- Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....
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- Find sum(r=1)^(10) cos^(3) rpi/3.
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- Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha...
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- Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...
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- If A + B + C = pi, prove that cos A cosec B cosec C + cos B cosec C c...
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- Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...
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- Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.
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- If A +B+C = 180^circ, prove that cos A/2+ cos B/2 +cos C/2 = 4cos (p...
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- If alpha + beta- gamma= pi, prove that sin^(2)alpha + sin^(2)beta - s...
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- If alpha + beta + gamma = 2 theta, prove that cos theta + cos(theta- ...
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- If A + B + C = pi, show that cot A + sinA/(sin B sin C) = cot B + sin...
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- If A + B + C = 0, prove that sum sin 2A = 2sum sin A * (1 + sum cos A...
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- Prove that tan(x - y) + tan(y - z) + tan(z - x) = tan(x - y) *tan(y -...
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