No links please Q 15 If y=cot-11+x-1-x1+x+1-x, show that, dydxx=12=-13 - Maths - Relations and Functions

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Q 15 If y = c o t - 1 1 + x - 1 - x 1 + x + 1 - x , show that, d y
d x x = 1 2 = - 1 3

Varun Rawat · Accepted Answer

We have,y = cot-11+x - 1-x1+x + 1-xPut x = cos 2θy = cot-11 + cos 2θ - 1 - cos 2θ1 + cos 2θ + 1 - cos 2θ⇒y = cot-12 cos2θ - 2 sin2θ2 cos2θ + 2 sin2θ⇒y = cot-12 cos θ - 2 sin θ2 cos θ + 2 sin θ⇒y = cot-1cos θ - sin θcos θ + sin θ⇒y = cot-1cos θcos θ - sin θcos θcos θcos θ + sin θcos θ⇒y = cot-11 - tan θ1 + tan θ⇒y =cot-1tanπ/4 - tan θ1 + tanπ/4  tan θ⇒y = cot-1tanπ4-θ⇒y = cot-1cotπ2 - π4-θ⇒y = π4+θ⇒y = π4 + 12cos-1x⇒dydx = 0 - 121-x2⇒dydx = -121-x2⇒dydxx=12 = -121 - 14 = -13

No links please Q.15. If y = c o t - 1 1 + x - 1 - x 1 + x + 1 - x , show that, d y d x x = 1 2 = - 1 3

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Q.15. If $y = c o t^{- 1} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}}$ , show that, ${[\frac{d y}{d x}]}_{x = \frac{1}{2}} = - \frac{1}{\sqrt{3}}$