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Differentiating both sides w.r.t x, we get d y d x × ln cos x + y × − sin x cos x = ln cos y + x × − sin y cos y × d y d x ∴ d y d x = ln cos y + y tan x ln cos x + x tan y

If cos x cos θ + sin x sin θ = cos y cos θ + sin y sin θ = 1, where x − y ≠ n π, n ∈ z, then cos x cos y cos 2 θ + sin x sin y sin 2 θ = View Solution Q 5

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Let us take a circle of radius one and let us take 2 points P and Q such that P is at an angle x and Q at an angle y as shown in the diagram Therefore, the co-ordinates of P and Q are P ( cos x , sin x ) , Q ( cos y , sin y )

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i) If y = a x a x... ∞, then prove that d y d x = y 2 log y x (1 − y log x log y) ii) If y = cos x cos x cos x cos x . . . ∞ , then prove that d y d x = − y 2 tan x 1 − y log cos x View Solution

Let sin x and sin y be roots of the quadratic equation a sin 2 θ + b sin θ + c = 0 (a, b, c ∈ R and a ≠ 0) such that sin x + 2 sin y = 1, then the value of (a 2 + 2 b 2 + 3 a b + a c) equals View Solution

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